Even with the answer key, many students make the same errors. Here’s what to watch for:
Parent: ( y = 2^x )
in the exponent is negative, the graph reflects over the . Practice Problem Walkthrough Even with the answer key, many students make the same errors
The base function 2ˣ grows upward. The negative sign flips it downward. The +3 shifts the asymptote to y = 3, but since it's flipped, the graph is below that asymptote. The negative sign flips it downward
, where b > 0 and b ≠ 1. (Common bases: 2, 3, 10, or e). (Common bases: 2, 3, 10, or e)
worksheet, here are the functions representing specific transformations: Course Hero Parent Function Transformation Description Transformed Function 2 to the x-th power Move 3 units up 8 to the x-th power Move 1 unit down 5 to the x-th power Move 2 units right 3 to the x-th power Move 4 units left 6 to the x-th power Move 2 units down Move 5 units right 4 to the x-th power Vertical compression by factor of 3 to the x-th power Vertical stretch by factor of 5 2 to the x-th power Compress vertically by , move 3 right, 2 up Visualizing Exponential Transformations The following plot demonstrates how a parent function changes when shifted vertically ( ) or reflected. Key Characteristics to Remember
Which equation matches a graph with y-intercept 2, asymptote y = –1, and increasing behavior?
