Special Functions - Pre-Calculus

Card 0 of 36

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

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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$

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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$

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

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We evaluate for

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

If is the greatest integer function, what is the value of ?

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The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was , we are looking for an integer less than this, which must be since any smaller integer would by definition not be "greatest".

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

Tap to see back →

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$

Tap to see back →

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$

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

Tap to see back →

We evaluate for

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

If is the greatest integer function, what is the value of ?

Tap to see back →

The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was , we are looking for an integer less than this, which must be since any smaller integer would by definition not be "greatest".

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

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

Tap to see back →

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$

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

Tap to see back →

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 ?

Tap to see back →

We evaluate for

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

If is the greatest integer function, what is the value of ?

Tap to see back →

The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was , we are looking for an integer less than this, which must be since any smaller integer would by definition not be "greatest".

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

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

Tap to see back →

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$

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

Tap to see back →

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 ?

Tap to see back →

We evaluate for

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

If is the greatest integer function, what is the value of ?

Tap to see back →

The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was , we are looking for an integer less than this, which must be since any smaller integer would by definition not be "greatest".

For the function defined below, what is the value of when ?

$f(x)=\left\{\begin{matrix} -x+1&$\text{ for }$x<1\ $x^{2}$-2&$\text{ for }$1< x< 3\ $2^{x}$&$\text{ for }$x\geq 3 \end{matrix}$

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Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .

For the function defined below, what is the value of when ?

$f(x)=\left\{\begin{matrix} -x+1&$\text{ for }$x<1\ $x^{2}$-2&$\text{ for }$1< x< 3\ $2^{x}$&$\text{ for }$x\geq 3 \end{matrix}$

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Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .

Let

$y=\left\{\begin{matrix} 2x&x\leq 0\ x+9& x>0 \end{matrix}\right.$

What does equal when ?

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Because 3>0 we plug the x value into the bottom equation.

Let

$y=\left\{\begin{matrix} 2x&x\leq 0\ x+9& x>0 \end{matrix}\right.$

What does equal when ?

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Because 3>0 we plug the x value into the bottom equation.