Question

Which graph represents the function h(x) = |x| + 0.5?

Answer 1

Answer:

Graph (3) is the correct representation of the function $h(x)$.

Step-by-step explanation:

Modulus function: A function which gives the absolute value or magnitude of a number or variable is termed as modulus function.

$|x|=\left\{\begin{array}{cc}x& if\ x\geq 0\\-x&if\ x < 0\end{array}$

Consider the given modulus function as follows:

$h(x)=|x|+0.5$

Then,

$|x|+0.5=\left\{\begin{array}{cc}x+0.5& if\ x+0.5\geq 0\\-x+0.5&if\ x +0.5 < 0\end{array}$

Simplify as follows:

$|x|+0.5=\left\{\begin{array}{cc}x+0.5& if\ x\geq -0.5\\-x+0.5&if\ x < -0.5\end{array}$

So, $h(x)=\left\{\begin{array}{cc}x+0.5& if\ x\geq -0.5\\-x+0.5&if\ x < -0.5\end{array}$

Graph (1): It is the graph of the function $|x|+1.5$.

Thus, graph is not the correct representation of the given function.

Graph (2): It is the graph of the function $|x+0.5|$.

Thus, graph is not the correct representation of the given function.

Graph (3): It is the graph of the function $|x|+0.5$.

Thus, graph is the correct representation of the given function.

Graph (4): It is the graph of the function $|x+1.5|$.

Thus, graph is not the correct representation of the given function.

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