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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∻Solution by Steps∻ ### (a) $f(x)$ is shifted 5 units downward. $y=$ ‖ step 1 ⋮ Start with the original function: $f(x) = 9^x$ ‖ ‖ step 2 ⋮ To shift the function 5 units downward, subtract 5 from the function: $y = 9^x - 5$ ‖ ∻Answer∻ ⚹ $y = 9^x - 5$ ⚹ ### (b) $f(x)$ is shifted 2 units to the left. $y=$ ‖ step 1 ⋮ Start with the original function: $f(x) = 9^x$ ‖ ‖ step 2 ⋮ To shift the function 2 units to the left, replace $x$ with $x + 2$: $y = 9^{x + 2}$ ‖ ∻Answer∻ ⚹ $y = 9^{x + 2}$ ⚹ ### (c) $f(x)$ is reflected about the $x$-axis. $y=$ ‖ step 1 ⋮ Start with the original function: $f(x) = 9^x$ ‖ ‖ step 2 ⋮ To reflect the function about the $x$-axis, multiply the function by $-1$: $y = -9^x$ ‖ ∻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 equation of the graph that results when $f(x)$ is reflected about the $x$-axis⍭ Generate me a similar question◊

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