suppose the graph of f is given. write an equation for each graph described that is obtained from the graph of f. (a) shift 5 units upward. $\bigcirc$ $y = f(x) - 5$ $\bigcirc$ $y = 5f(x)$ $\bigcirc$ $y = \frac{1}{5}f(x)$ $\bigcirc$ $y = f(x - 5)$ $\bigcirc$ $y = f(x) + 5$ (b) shift 5 units downward. $\bigcirc$ $y = f(x) - 5$ $\bigcirc$ $y = 5f(x)$ $\bigcirc$ $y = \frac{1}{5}f(x)$ $\bigcirc$ $y = f(x - 5)$ $\bigcirc$ $y = f(x) + 5$ (c) shift 5 units to the right. $\bigcirc$ $y = f(x - 5)$ $\bigcirc$ $y = f(x) - 5$ $\bigcirc$ $y = \frac{1}{5}f(x)$ $\bigcirc$ $y = f(x) + 5$ $\bigcirc$ $y = 5f(x)$ (d) shift 5 units to the left. $\bigcirc$ $y = f(x) + 5$ $\bigcirc$ $y = f(x + 5)$ $\bigcirc$ $y = \frac{1}{5}f(x)$

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Accepted Answer

# Explanation:
## Step1: Recall vertical shift up rule
For a vertical upward shift of $k$ units, the equation is $y = f(x) + k$. Here $k=5$, so $y = f(x) + 5$.
## Step2: Recall vertical shift down rule
For a vertical downward shift of $k$ units, the equation is $y = f(x) - k$. Here $k=5$, so $y = f(x) - 5$.
## Step3: Recall horizontal shift right rule
For a horizontal shift right of $k$ units, the equation is $y = f(x - k)$. Here $k=5$, so $y = f(x - 5)$.
## Step4: Recall horizontal shift left rule
For a horizontal shift left of $k$ units, the equation is $y = f(x + k)$. Here $k=5$, so $y = f(x + 5)$.

# Answer:
(a) $y = f(x) + 5$
(b) $y = f(x) - 5$
(c) $y = f(x - 5)$
(d) $y = f(x + 5)$

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Question

Explanation:

Step1: Recall vertical shift up rule

Step2: Recall vertical shift down rule

Step3: Recall horizontal shift right rule

Step4: Recall horizontal shift left rule

Answer: