Question

Math

Posted 2 months ago

```
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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Answer from Sia

Posted 2 months ago

Solution by Steps

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 $-1$.

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