Answer
$a.\quad -7$ and $1$
$b.\quad -3 $ and $5.$
$c.\quad -5 $ and $3.$
$d.\quad -3 $ and $5$
Work Step by Step
$(-5,0)$ and $(3,0)$ are points on the graph of y=f(x).
$a.$
The graph of f(x) is translated to the left by 2 units, so the new intercept points are
$(-5-2,0)$ and $(3-2,0)$
x-intercepts: $-7 $ and $1$
$b.$
The graph of f(x) is translated to the right by 2 units, so the new intercept points are
$(-5+2,0)$ and $(3+2,0)$
x-intercepts: $-3 $ and $5.$
$c.$
The graph of f(x) is vertically stretched, so the new intercept points are
$(-5,0\cdot 2)$ and $(3,0\cdot 2)$
x-intercepts: $-5 $ and $3.$
$d.$
The graph of f(x) is reflected about the y-axis, so the new intercept points are
$(-(-5),0)$ and $(-3,0)$
x-intercepts: $-3 $ and $5.$
