Special Functions

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Pre-Calculus › Special Functions

Questions 1 - 10

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

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

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 ?

-13

-7

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

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

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

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 ?

-13

-7

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

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

Explanation

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".