Question

Explain in writing how the graph of the function h(x) = -|x-1| +4 is related to the graph of oneof the six basic functions. Sketch a graph of h(x). (6 points

Answer 1

Notice that the expression for h(x) uses an absolute value. The absolute value is the basic function related to h(x).

Recall the following function transformations:

Horizontal shift by c units:

$f(x)\rightarrow f(x-c)$

Vertical shift by c units:

$f(x)\rightarrow f(x)+c$

Reflection across the X axis:

$f(x)\rightarrow-f(x)$

Starting with the absolute value function, notice that the function h can be obtained by applying a reflection across the X-axis, a horizontal shift by 1 unit and a vertical shift by 4 units:

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