Answers Advanced Algebra Concepts and ConnectionsExponential and Logarithmic Functions: Part One

Exponential and Logarithmic Functions: Part One — Test Answers

25 verified answers3 views

If f of x and its inverse function, f inverse of x , are both plotted on the same coordinate plane, where is their point of intersection?

open paren 1 comma 4 close paren

open paren 3 comma 0 close paren

open paren 0 comma 6 close paren

open paren 2 comma 2 close paren

Free Preview

If f of x and its inverse function, f inverse of x , are both plotted on the same coordinate plane, what is their point of intersection?

open paren 3 comma 3 close paren

open paren 0 comma negative 2 close paren

open paren 2 comma 0 close paren

open paren 1 comma negative 1 close paren

If f of x is equal to 1 ninth x minus 2 , what is f inverse of x ?

f inverse of x is equal to negative 2 x plus 1 ninth

f inverse of x is equal to 9 x plus 2

f inverse of x is equal to 1 ninth x plus 2

f inverse of x is equal to 9 x plus 18

If g of x is equal to the fraction with numerator x plus 1 and denominator x minus 2 and h of x is equal to 4 minus x , what is the value of open paren g circ h close paren times negative 3 ?

15 halves

18 fifths

5 halves

8 fifths

Which function has an inverse that is a function?

d times x is equal to negative 9

p times x is equal to absolute value of x

b times x is equal to x squared plus 3

m times x is equal to negative 7 x

Fifteen percent of an employee’s taxable income is collected each paycheck. Before taxes are removed from each paycheck, 350 dollars of tax-exempt expenses is taken out. If the variable x represents the employee’s pay before tax-exempt expenses and taxes are removed, which expression represents the employee’s take-home pay after these deductions?

x minus 0 point 1 5 minus 350

x minus 0 point 8 5 minus 350

0 point 8 5 times open paren x minus 350 close paren

0 point 1 5 times open paren x minus 350 close paren

If h of x is equal to 6 minus x , what is the value of open paren h circ h close paren times 10 ?

negative 2

negative 4

Which function has an inverse that is also a function?

k times x is equal to negative 9 x squared

w times x is equal to negative 20

g of x is equal to 2 x minus 3

f of x is equal to start absolute value x plus 2 end absolute value

Which statement could be used to explain why f of x is equal to 2 x minus 3 has an inverse relation that is a function?

The graph of f of x passes the vertical line test.

f of x is not a function.

The graph of the inverse of f of x passes the horizontal line test.

f of x is a one-to-one function.

If f of x is equal to x squared plus 1 and g of x is equal to x minus 4 , which value is equivalent to open paren f circ g close paren times 10 ?

126

606

A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function m times x , where x is the length of the radius of the circle in feet. The homeowner estimates that he will pay 1 point 5 0 dollars per square foot of mulch. This cost is represented by the function g of m , where m is the area requiring mulch. m times x is equal to pi x squared minus 2 square root of 2 x squared g of m is equal to 1 point 5 0 m Which expression represents the cost of the mulch based on the radius of the circle?

1 point 5 0 times open paren pi x squared minus 2 square root of 2 x squared close paren

1 point 5 0 times open paren pi times 1 point 5 0 x squared minus 2 square root of 2 1 point 5 0 x squared close paren

pi times 1 point 5 0 x squared minus 2 square root of 2 x squared

pi times 1 point 5 0 x squared minus 2 square root of 2 1 point 5 0 x squared

Which graph shows a function whose inverse is also a function?

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 5 to 5 with an increment of 1. The function f(x) is represented by a red curve starting at the origin "0 comma 0", curving steeply upward to "1 comma 1", and then flattening out as it passes through "4 comma 2" before continuing to the right with an arrowhead. The inverse function f superscript (-1) (x) is represented by a blue curve starting at the origin "0 comma 0", staying relatively flat until it intersects the red curve at "1 comma 1", and then curving steeply upward through "2 comma 4" before continuing upward with an arrowhead.

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 5 to 5 with an increment of 1. The function f(x) is a blue, sharp-peaked curve with its highest point (vertex) at "1 comma 3". From the vertex, one ray extends downward and to the left, passing through "0 comma negative 3" with an arrowhead pointing down. The other ray extends downward and to the right, passing through "2 comma negative 3" with an arrowhead pointing down.The inverse function f superscript {-1} (x) is a red, sideways sharp-peaked curve with its rightmost point (vertex) at "3 comma 1". From this vertex, one ray extends to the left and slightly upward, passing through "negative 3 comma 2" with an arrowhead pointing left. The other ray extends to the left and slightly downward, passing through "negative 3 comma 0" with an arrowhead pointing left.

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 5 to 5 with an increment of 1. The function f(x) is a blue parabola that opens upward with its vertex located on the y-axis at "0 comma negative 2". It passes through the x-axis near "negative 1 comma 0" and "1 point 0", and extends upward through "negative 1 point 2 comma 1" and "1 point 2 comma 1" with arrowheads pointing up on both ends.The inverse function f superscript {-1}(x) is a red parabola that opens to the right with its vertex located on the x-axis at " negative 2 comma 0". It passes through the y-axis near "0 comma negative 1" and "0 comma 1", and extends horizontally to the right through "1 comma negative 1 point 2" and "1 comma 1 point 2" with arrowheads pointing right on both ends.

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 5 to 5 with an increment of 1. The function f(x) is a blue curve that enters from the bottom-left, passing near "negative 1 comma negative 3" and rising steeply. It creates a local maximum at "0 comma 2", dips down to a local minimum at "1 comma 1", and then rises sharply toward the top right, passing through "1 point 2 comma 4" with an arrowhead pointing upward. The inverse function f superscript {-1} (x) is a red curve that enters from the far left near " negative 4 comma negative 1" and proceeds horizontally to the right. It curves upward and backward to form a local maximum on the right side at "2 comma 0", snakes back to the left to hit a local minimum at "0 point 6 comma 1", and then levels off to the right, exiting past "4 comma 1 point 2" with an arrowhead pointing right.

Which statement could be used to explain why the function h of x is equal to x cubed has an inverse relation that is also a function?

The graph of h of x passes the horizontal line test.

The graph of the inverse of h of x passes the horizontal line test.

The graph of the inverse of h of x is a vertical line.

The graph of h of x passes the vertical line test.

If c times x is equal to 4 x minus 2 and d times x is equal to x squared plus 5 x , what is open paren c circ d close paren times x ?

4 x squared plus 20 x minus 2

16 x squared plus 4 x minus 6

x squared plus 9 x minus 2

4 x cubed plus 18 x squared minus 10 x

Which of the following is an odd function?

f of x is equal to square root of x

f of x is equal to x cubed plus 5 x squared plus x

f of x is equal to negative x

f of x is equal to x squared plus x

If A times x is equal to 3 x plus 1 and b times x is equal to square root of x minus 4 end root , what is the domain of open paren b circ A close paren times x ?

left bracket 0 comma infinity right parenthesis

left bracket 4 comma infinity right parenthesis

left bracket 1 comma infinity right parenthesis

open paren negative infinity comma infinity close paren

If f of x is an even function and open paren 6 comma 8 close paren is one the points on the graph of f of x , which reason explains why open paren negative 6 comma 8 close paren must also be a point on the graph?

The graph has rotational symmetry, so the point will be reflected across the y -axis.

The graph has rotational symmetry, so the point will be rotated 90 degrees about the origin.

Since the function is even, the outputs of a negative x -value and a positive x -value are the same.

Since the function is even, the outputs of a negative y -value and a positive y -value are the same.

Which graph represents an odd function?

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 8 points. The points are (negative 4 comma 2), (negative 3 comma negative 1), (negative 1 comma negative 3), (0 comma 1), (1 comma 0), (2 comma negative 4), (4 comma 5), and (5 comma 4).

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 8 points. The points are (negative 4 comma 0), (negative 3 comma 1), (negative 2 comma negative 3), (negative1 comma negative 2), (1 comma 2), (2 comma 3), (3 comma negative 1), and (4 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 6 points. The points are (negative 5 comma 3), (negative 3 comma 1), (negative 1 comma 1), (1 comma 3), (3 comma negative 5), (5 comma negative 1).

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 11 points. The points are (negative 4 comma 3), (negative 4 comma 4), (negative 3 comma 5), (negative 2 comma 1) , (negative 1 comma negative 1), (0 comma negative 3), (1 comma negative 1), (2 comma 1), (3 comma 5), (4 comma 3), and (4 comma 4).

Which graph shows a function whose inverse is also a function?

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, 2 lines are shown. A curve labeled f of (x) has a positive slope and goes through (negative 4 comma negative 3), (0 comma negative 1), and (2 comma 0). Another curve labeled inverse of f of (x) has a positive slope and goes through (negative 2 comma negative 2), (negative 1comma 0), and (0 comma 2).

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, 2 v-shaped graphs are shown. A v-shaped graph labeled f of (x) opens up and goes through (negative 1 comma 5), has a vertex at (1 comma 1), and goes through (3 comma 5). Another v-shaped graph labeled inverse of f of (x) opens right and goes through (5 comma 3), has a vertex at (1 comma 1), and goes through (3 comma 0).

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, two curved graphs are shown. A curve labeled f of (x) sharply increases from (negative 0 point 5 comma negative 5) to (0 comma negative 2) and then sharply changes directions and curves down to (0 point 5 comma negative 3 point 5). The curve then sharply changes direction and goes up through (1 comma 0). Another curve labeled inverse of f of (x) curves slightly up from (negative 5 comma negative 0 point 5) to (negative 2 comma 0). The curve then sharply changes directions and go to the left toward (negative 3 point 5 comma 1). The curve then changes directions and goes through (0 comma 1) and gradually increases.

Image with description On a coordinate plane with x and y axes marked from negative 5 to 5, 2 parabolas are shown. A curve labeled f of (x) opens down and goes through (negative 1 comma negative 5), has a vertex at (0 comma 1), and goes through (1 comma negative 5). Another curve labeled inverse of f of (x) opens to the left and goes through (negative 5 comma 1), has a vertex at (1 comma 0), and goes through (negative 5 comma negative 1).

If h of x is the inverse of f of x , what is the value of h of f of x ?

f of x

Did you find these answers helpful?

Exponential and Logarithmic Functions: Part One — Test Answers

More from this Course

TRY EDGENUITY HACKS