Let f(x)=|x+9|+4. Write a function g whose graph is a vertical shrink of the graph of f by a factor of 1/5

Answer 1

The vertex form of an absolute value function can represented as f(x) = a|x-h|+k

Remember how a, h and k transform the graph of a function:

a vertically stretches a graph (when |a| is greater than 1) or vertically compresses a graph (when |a| is between the values of 0 and 1). a also reflects the graph over the x-axis if a is negative

h translates (or shifts) the graph horizontally (left or right)

k translates (or shifts) the graph vertically (up or down)

This problem asks for a vertical "shrink" which is the same as a compression. We simply need multiply the a value in the equation by 1/5.

a = 1 in this equation and can be written:

f(x) = 1 |x+9| + 4 Multiply the a value by 1/5

g(x) = 1/5 |x+9| + 4