Starting with the graph of $f(x)=9^{x}$, write the equation of the graph that results when:
(a) $f(x)$ is shifted 5 units downward. $y=$
(b) $f(x)$ is shifted 2 units to the left. $y=$
(c) $f(x)$ is reflected about the $x$-axis. $y=$

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Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To shift the graph of $f(x) = 9^x$ 5 units downward, we subtract 5 from the function. ‖ ‖ step 2 ⋮ The new equation is $y = 9^x - 5$. ‖ ∻Answer∻ ⚹ $y = 9^x - 5$ ⚹ ‖ step 1 ⋮ To shift the graph of $f(x) = 9^x$ 2 units to the left, we replace $x$ with $x + 2$. ‖ ‖ step 2 ⋮ The new equation is $y = 9^{x + 2}$. ‖ ∻Answer∻ ⚹ $y = 9^{x + 2}$ ⚹ ‖ step 1 ⋮ To reflect the graph of $f(x) = 9^x$ about the $x$-axis, we multiply the function by -1. ‖ ‖ step 2 ⋮ The new equation is $y = -9^x$. ‖ ∻Answer∻ ⚹ $y = -9^x$ ⚹ ∻Key Concept∻ ⚹Graph Transformations⚹ ∻Explanation∻ ⚹Shifting a graph vertically involves adding or subtracting a constant to the function. Shifting horizontally involves replacing $x$ with $x + c$ or $x - c$. Reflecting about the $x$-axis involves multiplying the function by -1.⚹◊What is the transformation formula for shifting a function $f(x)$ 5 units downward?⍭ Generate me a similar question◊

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