Question

The black graph is y = f(x). Choose the equation for the red graph.

A. y = f (x + 3)
B. y - 3 = f (x)
C. y + 3 = (x)
D. y = f (x - 3)​

Answer 1

Answer: C. y + 3 = f(x)

Explanation:

To find the red graph, we have to know about the transformations from f(x). The graph of f(x) is the absolute value parent function. So we are finding the transformation of the AV parent function.

A typical function transformation equation is
`f(x)=a(y-h)+k` where h controls how far left or right graph goes, k controls how far up or down the graph goes and a controls how narrow or wide the graph gets.

The red graph vertex is at the point (0,3) and f(x) vertex is at (0,0). Since we know the y value had gone up 3, we can add 3 to the graph.

k - controls the y value of the graph (up is +, down is -)

h - controls the x value of the graph (left is +, right is -)

a - controls the slope of the graph (a>1 or a>-1, a is narrower, 0<a<1 or 0>a>-1, a is wider).

Since we have our graph going up 3, it would be positive 3 added to the equation. Since k is outside the parenthesis, our transformation would be f(x)=y+3.

Hope that helped a lot.

:)

Answer 2

Hi,

Explanation:

Answer B: y=f(x)+3

rem f(x)=|x|