Absolute Value Functions

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Pre-Calculus › Absolute Value Functions

Questions 1 - 3

1

Which of the following is a point on the following function?

$y=\left | x^2-5x-56\right |+27$

Explanation

One way to approach this problem would be to plug in each answer and see what works. However, I would be a little more strategic and eliminate any options that don't make sense.

Our y value will never be negative, so eliminate any options with a negative y-value.

Try (0,0) really quick, since it's really easy

$y=\left | x^2-5x-56\right |+27 \rightarrow 0=\left|0^2-5(0)-56\right|+27=83 \rightarrow 0 eq 83$

The only point that makes sense is (5,83), therefore it is the correct answer

$y=\left | x^2-5x-56\right |+27 \rightarrow 83=\left|5^2-5(5)-56\right|+27=83 \rightarrow 83=83$

2

If $y=\left |x^3-5x^2+5 \right |$ , then what is the value of when ?

-13

-7

7

13

20

Explanation

We evaluate for

Since the absolute value of any number represents its magnitude from and is therefore always positive, the final answer would be

3

Evaluate: $\left | x-3\right |<15$

$-12\leq x\leq18$

$x\leq18$

Explanation

Cancel the absolute value sign by separating the function $\left | x-3\right |<15$ into its positive and negative counterparts.

Evaluate the first scenario.

Evaluate the second scenario.

The correct answer is:

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