Question

describe how the given equation represents a transformation of the function f(x):

• y = f(x)+7

left 7 units
right 7 units
up 7 units
down 7 units

• y = f(x + 7)-2

left 7 units and up 2 units
right 7 units and up 2 units
left 7 units and down 2 units
right 7 units and down 2 units
note: in order to get credit for this problem all answers must be correct.
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Explanation:

Step1: Analyze $y = f(x)+7$

For a function $y = f(x)+k$, when $k>0$, the graph of the function is shifted vertically upwards. Here $k = 7$, so the graph of $y=f(x)$ is shifted up 7 units.

Step2: Analyze $y = f(x + 7)-2$

For a function $y=f(x + h)+k$, when $h>0$, the graph is shifted left by $h$ units and when $k<0$, the graph is shifted down by $|k|$ units. Here $h = 7$ and $k=-2$, so the graph of $y = f(x)$ is shifted left 7 units and down 2 units.

Answer:

• $y = f(x)+7$: up 7 units
• $y = f(x + 7)-2$: left 7 units and down 2 units