Question

The graph shows the function f(x) = |x – h| + k. What is the value of h?h = –3.5h = –1.5h = 1.5h = 3.5

Answer 1

Given:

`f(x)=|x-h|+k`

The parent function is:

`y=|x|`

The graph of the parent function is:

The function f(x) given shows a vertical shift by h units to the left and a horizontal shift k units down.

Hence, the parent function was shifted by 1.5 units to the left and 3.5 units downwards to get the new function f(x).

Thus,

`\begin{gathered} y=|x| \\ \\ The\text{ transformation shown on the graph is:} \\ f(x)=|x+1.5|-3.5 \\ \\ Comparing\text{ the equation to the given function;} \\ f(x)=|x-h|+k \\ -h=1.5,\text{ }k=-3.5 \\ h=-1.5,k=-3.5 \end{gathered}`

Therefore, the value of h = - 1.5