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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Piecewise Functions

Determine the value of f(1) if the function is

$f(x)=\left\{\begin{matrix} x& x<3\\ \pi&x=3 \\ 4&x>3 \end{matrix}\right.$

Possible Answers:

f(1)=1

f(1)=3

f(1)=4

$f(1)=\pi$

Correct answer:

f(1)=1

Explanation:

In order to determine the value of f(1) of the function we set x=1.

The value comes from the function in the first row of the piecewise function, and as such

f(1)=1

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Example Question #1 : Piecewise Functions

Determine the value of f(1) if the function is

$f(x)=\left\{\begin{matrix} \sqrt{x}& 0\leq x<4\\ \3&x=4 \\ e^{-x}&x>4 \end{matrix}\right.$

Possible Answers:

$f(1)=\frac{1}{e}$

f(1)=3

f(1)=1

f(1)=3

Correct answer:

f(1)=1

Explanation:

In order to determine the value of f(1) of the function we set x=1.

The value comes from the function in the first row of the piecewise function, and as such

$f(1)=\sqrt{1}=1$

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Example Question #1 : Piecewise Functions

For the function f(x) defined below, what is the value of f(x) when x=3 ?

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

Possible Answers:

-2

Correct answer:

Explanation:

Evaluate the function for x=3 . Based on the domains of the three given expressions, you would use $2^{x}$ , since is greater than or equal to .

$2^{x}=2^{3}=8$

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Example Question #1 : Special Functions

If is the greatest integer function, what is the value of F(2.4) ?

Possible Answers:

2.5

Correct answer:

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 2.4 , we are looking for an integer less than this, which must be since any smaller integer would by definition not be "greatest".

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Example Question #981 : Pre Calculus

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

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

Possible Answers:

(0,0)

(5,83)

(5,-43)

(-27,-27)

(14,36)

Correct answer:

(5,83)

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

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

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Example Question #982 : Pre Calculus

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

Possible Answers:

$x\leq18$

-12,18

x<18

-12<x<18

$-12\leq x\leq18$

Correct answer:

-12<x<18

Explanation:

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

x-3<15

-(x-3)<15

Evaluate the first scenario.

x-3<15

x<18

Evaluate the second scenario.

-(x-3)<15

x-3>-15

x>-12

The correct answer is:

-12<x<18

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Example Question #982 : Pre Calculus

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

Possible Answers:

-13

-7

Correct answer:

Explanation:

We evaluate for x=3

y=|(3)^3-5(3)^2+5|

y=|27-45+5|

y=|-13|

Since the absolute value of any number represents its magnitude from and is therefore always positive, the final answer would be y=13

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Example Question #1 : Evaluate Functions

Given f(x) and h(x) , evaluate f(h(7)) .

f(x)=5x^2-13x+8

h(x)=x^3-343

Possible Answers:

343

Correct answer:

Explanation:

We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

h(x)=x^3-343

h(7)=7^3-343=343-343=0

Now that we know h(7), we go ahead and plug it into f(x).

f(x)=5x^2-13x+8

$f(0)=5\cdot 0^2-13\cdot 0+8=8$

So our final answer is simply 8.

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Example Question #2 : Evaluate Functions

Solve the function. $\frac{10x^2-10}{x-1}=0$

Possible Answers:

$\pm \frac{1}{10}$

$\pm1$

Correct answer:

Explanation:

Determine the domain of $\frac{10x^2-10}{x-1}=0$ .

$x\neq1$

Multiply x-1 on both sides of the equation to cancel the denominator and divide the equation 10x^2-10=0 by ten.

x^2-1=0

x^2=1

$x= \pm1$

Since the domain states that $x\neq1$ , the only possible answer is x= -1 .

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Example Question #1 : Evaluate Functions

Solve for : 9^x+1=4

Possible Answers:

$\frac{4}{9}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{2}$

Explanation:

Rewrite 9^x+1=4 so that the exponential variable is isolated.

9^x=3

Reconvert 9^x=3 to a similar base. Use exponents to redefine the terms.

3^2^x=3^1

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

2x=1

Solve for .

$x=\frac{1}{2}$

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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Piecewise Functions

Example Question #1 : Piecewise Functions

Example Question #1 : Piecewise Functions

Example Question #1 : Special Functions

Example Question #981 : Pre Calculus

Example Question #982 : Pre Calculus

Example Question #982 : Pre Calculus

Example Question #1 : Evaluate Functions

Example Question #2 : Evaluate Functions

Example Question #1 : Evaluate Functions

All Precalculus Resources

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