What is the value of h(-8) if h(x) = |2x + 7|?
Understand the Problem
The question is asking for the evaluation of the function h(x) = |2x + 7| at the input x = -8. To solve it, we will substitute -8 into the function and simplify the expression to find the value of h(-8).
Answer
$h(-8) = 9$
Answer for screen readers
The value of $h(-8)$ is $9$.
Steps to Solve
- Substitute the value into the function
We start by substituting $x = -8$ into the function $h(x) = |2x + 7|$.
$$ h(-8) = |2(-8) + 7| $$
- Calculate the expression inside the absolute value
Now we calculate the expression $2(-8) + 7$.
$$ 2(-8) = -16 $$
So,
$$ -16 + 7 = -9 $$
- Evaluate the absolute value
Next, we take the absolute value of the result we just calculated.
$$ h(-8) = |-9| $$
- Determine the absolute value
The absolute value of $-9$ is $9$.
Thus,
$$ h(-8) = 9 $$
The value of $h(-8)$ is $9$.
More Information
The absolute value function $|x|$ returns the non-negative value of $x$. Thus, it is important to remember that any negative input will be converted to positive when evaluating an absolute value.
Tips
- Forgetting to apply the absolute value concept, which can lead to a negative answer instead of the correct positive answer.
- Miscalculating $2(-8)$ and not simplifying the expression correctly before applying the absolute value.
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