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Starting with the graph of \( f(x)=8^{x} \), write the equation of the graph that results from (a) shifting \( f(x) 3 \) units upward. \( y= \) (b) shifting \( f(x) 4 \) units to the left. \( y=\square \) (c) reflecting \( f(x) \) about the x-axis. \( y=\square \)

Ask by Wells Park. in the United States
Mar 14,2025

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**(a) Shifting \( f(x)=8^x \) three units upward:** \[ y = 8^x + 3 \] **(b) Shifting \( f(x)=8^x \) four units to the left:** \[ y = 8^{x+4} \] **(c) Reflecting \( f(x)=8^x \) about the x-axis:** \[ y = -8^x \]

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(a) To shift the graph of \( f(x) = 8^{x} \) upward by 3 units, you'd add 3 to the entire function. Therefore, the equation becomes \( y = 8^{x} + 3 \). (b) To shift the graph of \( f(x) = 8^{x} \) left by 4 units, you'd replace \( x \) in the function with \( x + 4 \). Thus, the equation becomes \( y = 8^{(x + 4)} \) or equivalently \( y = 8^{x} \cdot 8^{4} \). (c) Reflecting the graph of \( f(x) = 8^{x} \) about the x-axis means multiplying the function by -1. Therefore, the equation becomes \( y = -8^{x} \).

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