Answer:
Options a, c and d
Step-by-step explanation:
Given the parent function f(x) = x, and calling g(x) its transformation. In the plot we see the following equation: -3*x -1
<u>Option a</u>
reflect over the y-axis: g(x) = -x
then vertically stretch by a factor of 3: g(x) = -3*x
and then shift down 1 unit: g(x) = -3*x -1
<u>Option b</u>
Shift left 2 units: g(x) = x + 2
then reflect over the x-axis: g(x) = -x - 2
and then vertically stretch by a factor of 3: g(x) = -3*x - 2
<u>Option c</u>
reflect over the x-axis: g(x) = -x
then vertically stretch by a factor of 3: g(x) = -3*x
and then shift down 1 unit: g(x) = -3*x -1
<u>Option d</u>
Shift right 1 unit: g(x) = x - 1
then reflect over the y-axis: g(x) = -x - 1
and then vertically stretch by a factor of 3: g(x) = -3*x - 1
<u>Option e</u>
Shift right 1 unit: g(x) = x - 1
then reflect over the x-axis: g(x) = -x + 1
and then vertically stretch by a factor of 3: g(x) = -3*x + 1
<u>Option f</u>
Shift down 1 unit: g(x) = x - 1
then reflect over the x-axis: g(x) = -x + 1
and then vertically stretch by a factor of 3: g(x) = -3*x + 1