Question

guided practice
exponential functions
answer the following questions given the exponential function ( y = b^{x - h} + k ).
type your answer and then click or tap done.
will the graph of ( y = 0.5^{x + 2} - 1 ) translate left or right? type left or right.

Explanation:

Step1: Recall the transformation rule for exponential functions

For the exponential function \( y = b^{x - h}+k \), the horizontal shift is determined by the value of \( h \). If \( h>0 \), the graph shifts right by \( h \) units; if \( h < 0 \), the graph shifts left by \( |h| \) units.

Step2: Rewrite the given function in the form \( y = b^{x - h}+k \)

The given function is \( y=0.5^{x + 2}-1 \). We can rewrite the exponent as \( x-(- 2) \), so the function becomes \( y = 0.5^{x-(-2)}-1 \). Here, \( h=-2 \).

Step3: Determine the direction of the shift

Since \( h=-2<0 \), the absolute value of \( h \) is \( 2 \), and according to the transformation rule, when \( h < 0 \), the graph shifts left by \( |h| \) units. So the graph of \( y = 0.5^{x+2}-1 \) translates left.

Answer:

left