Question

Consider the function f(x)=|x+3|−5 and its graph, which follows. An absolute value function with vertex (negative 3, negative 5). It passes through (negative 8, 0) & (2, 0).© 2018 StrongMind. Created using GeoGebra. Suppose the function is transformed by the function g(x)=−15f(x).Select the correct graph of the transformation.

Answer 1

Answer:

See graph below (graphs not numbered/lettered)

Step-by-step explanation:

Given:

`f(x)\text{ = \mid x + 3\mid - 5}`

To find:

the graph of the function when it is -1/5f(x)

To determine the graph, we will pick points from the initial graph and apply the transformation -1/5f(x) to it

Using points: (-3, -5), (5, 3) and (-11, 3)

First, we apply a dilation with a scale factor of 1/5

We are multiplying the y coordinate by 1/5

(-3, -5) becomes (-3, -1)

(5, 3) becomes (5, 3/5)

(-11, 3) becomes (-11, 3/5)

Next, we will apply a reflection over the x axis. This will negate the y coordinate:

(-3, -1) becomes (-3, 1)

(5, 3/5) becomes (5, -3/5)

(-11, 3) becomes (-11, -3/5)

Plotting the points on the graph:

This graph in the option: