Absolute Value Functions - Pre-Calculus

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Question

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

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Answer

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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Question

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

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

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Answer

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\neq 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$

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Question

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

Tap to reveal answer

Answer

We evaluate for

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

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Question

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

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

Tap to reveal answer

Answer

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\neq 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$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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:

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

We evaluate for

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

← Didn't Know|Knew It →

Question

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

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

Tap to reveal answer

Answer

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\neq 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$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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:

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

We evaluate for

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

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

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:

← Didn't Know|Knew It →

Question

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

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

Tap to reveal answer

Answer

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\neq 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$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

We evaluate for

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

← Didn't Know|Knew It →

Knew It

Absolute Value Functions - Pre-Calculus

Evaluate:

Cancel the absolute value sign by separating the function into its positive and negative counterparts. Evaluate the first scenario. Evaluate the second scenario. The correct answer is:

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

If , then what is the value of when ?

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

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

Evaluate:

Cancel the absolute value sign by separating the function into its positive and negative counterparts. Evaluate the first scenario. Evaluate the second scenario. The correct answer is:

If , then what is the value of when ?

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

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

Evaluate:

Cancel the absolute value sign by separating the function into its positive and negative counterparts. Evaluate the first scenario. Evaluate the second scenario. The correct answer is:

If , then what is the value of when ?

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

Evaluate:

Cancel the absolute value sign by separating the function into its positive and negative counterparts. Evaluate the first scenario. Evaluate the second scenario. The correct answer is:

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

If , then what is the value of when ?

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

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

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:

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

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

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

We evaluate for

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

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

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

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

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:

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

We evaluate for

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

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

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

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

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:

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

We evaluate for

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

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

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:

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

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

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

We evaluate for

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