Question

the graph of $y = f(x)$ is given.
match each of the following equations with its graph.
(a) $y = f(x - 4)$
\\(\bigcirc\\) 1
\\(\bigcirc\\) 2
\\(\bigcirc\\) 3
\\(\bigcirc\\) 4
\\(\bigcirc\\) 5
(b) $y = f(x) + 3$
\\(\bigcirc\\) 1
\\(\bigcirc\\) 2
\\(\bigcirc\\) 3
\\(\bigcirc\\) 4
\\(\bigcirc\\) 5

Explanation:

Step1: Analyze horizontal shift for (a)

The transformation $y=f(x-4)$ shifts the graph of $f(x)$ 4 units right. The original $f(x)$ has a root at $x=3$; shifting right 4 units gives a root at $x=3+4=7$, which matches Graph 3.

Step2: Analyze vertical shift for (b)

The transformation $y=f(x)+3$ shifts the graph of $f(x)$ 3 units up. The original $f(x)$ has a y-intercept at $y=1$; shifting up 3 units gives a y-intercept at $y=1+3=4$, which matches Graph 1.

Answer:

(a) 3
(b) 1