Answer:
B
Step-by-step explanation:
The red graph is a horizontal translation of 5 units left, followed by a reflection in the x- axis, of the black graph.
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then shift to the left of a units
• If a < 0 then shift to the right of a units
Here the graph is shifted 5 units to the left, thus
f(x) → f(x + 5)
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Note the y- coordinate of the image is the negative of the original
Note that [tex]\frac{y}{-1}[/tex] = - y, thus
The equation of the red graph is
[tex]\frac{y}{-1}[/tex] = f(x + 5) → B
