Exponential and Logarithmic Functions — Test

Question 17 • Algebra II

Which of the following shows the graph of y is equal to 4 to the x th power plus 3 ?

Answer

Image with description On a coordinate plane, the curve passes through (3 comma 1) and (4 comma 4).It increases rapidly in the first quadrant as x increase and goes towards line y equal 0 as x decreases in the second quadrant.

Image with description On a coordinate plane, the curve passes through (negative 3 comma 1) and (negative 2 comma 4).It increases rapidly in the first quadrant as x increase and goes towards line y equal 0 as x decreases in the second quadrant.

Image with description On a coordinate plane, the curve passes through (0 comma 4) and (1 comma 7).It increases rapidly in the first quadrant as x increase and goes towards line y equal 3 as x decreases in the second quadrant.

Image with description On a coordinate plane, the curve passes through (0 comma negative 2) and (1 comma 1).It increases rapidly in the first quadrant as x increase and goes towards line y equal negative 3 as x decreases in the third quadrant.

Explanation

For y = 4^x + 3, substituting x = 0 gives y = 1 + 3 = 4, and substituting x = 1 gives y = 4 + 3 = 7. The graph also approaches the horizontal line y = 3 as x decreases, because 4^x approaches 0. Choice C has these points and this horizontal asymptote.

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