Vertical Stretches and Shrinks of Exponential Functions

Question 1

Which statements are true about the graph? Check all that apply.The y-intercept is (0, 2).The x-intercept is (4, 0).f(1) = 2f(2) = 8It is a shrink of an exponential growth function.

Revolt · Accepted Answer

The y-intercept is (0, 2).; f(2) = 8

Question 2

Sample Response: When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a. What did you include in your response? Check all that apply.Any number to the power of 0 equals 1.Any number times 1 equals the number.Multiplying the value of a by 1 will equal the

Revolt · Accepted Answer

Any number to the power of 0 equals 1.; Any number times 1 equals the number.; Multiplying the value of a by 1 will equal the initial value.

Question 3

The initial value of the function is[___].

Revolt · Accepted Answer

2; The initial value of the function is.: 2; The base of the function is.: 3; The function shows exponential.: growth

Question 4

The equation for this function is

Revolt · Accepted Answer

✔ 8; f(x) = ()x.: 8; f(x) = ()x.: 0.5

Question 5

Question 77590

Revolt · Accepted Answer

77590

Question 6

Explain why the initial value of any function of the form f(x) = a(bx) is equal to a.

Revolt · Accepted Answer

To find the initial value, we evaluate the function at x = 0. Substituting 0 for x in the equation f(x) = a(b^x) gives f(0) = a(b^0). Since any non-zero number raised to the zero power is 1, the expression simplifies to f(0) = a(1). Multiplying any number by 1 results in that number, so f(0) = a. Thus, the initial value is always a.

Question 7

Fiona started her study of bacteria growth with 1,000 bacteria in a petri dish. After 1 hour, the count was increased to 1,800. After 2 hours, the count was 3,240. After the third hour showed a count of 5,832, Fiona wrote an equation to represent the exponential growth of the bacteria. What exponential growth function did Fiona write?

Revolt · Accepted Answer

✔ 1000; f(x) = ( )x: 1000; f(x) = ( )x: 1.8

Question 8

Consider the function f(x) = One-third (6)x. What is the value of the growth factor of the function?

Revolt · Accepted Answer

6

Question 9

Which is a stretch of an exponential decay function?

Revolt · Accepted Answer

f(x) = 5

Question 10

Which point is on the graph of the function f(x) = (2)x?

Revolt · Accepted Answer

(1, 1)

Vertical Stretches and Shrinks of Exponential Functions Answers

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