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Algebra 1 : Functions and Lines

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : Algebraic Functions

Given a function $f(x)=\frac{x^{2}-4x+11}{2}$ , what is f(7) ?

Possible Answers:

Correct answer:

Explanation:

Given a function

$f(x)=\frac{x^{2}-4x+11}{2}$ ,

we can plug in x=7 to get

$f(7)=\frac{(7)^{2}-4(7)+11}{2}=\frac{49-28+11}{2}=\frac{21+11}{2}=\frac{32}{2}=16$ .

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Example Question #73 : Algebraic Functions

Solve for : x-7=7 .

Possible Answers:

Correct answer:

Explanation:

In order to solve for in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to that is the inverse (opposite) of what's currently being applied to .

Given x-7=7 , we see that is being subtracted from , so we need to add to both sides of the equation to isolate :

x-7=7

x-7+7=7+7

x=14

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Example Question #74 : Algebraic Functions

Given a function $f(x)=-x^{2}-\frac{1}{x}+3x$ , what is f(2) ?

Possible Answers:

$\frac{3}{2}$

$\frac{5}{2}$

$\frac{1}{2}$

$-\frac{1}{2}$

$\frac{7}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

Given a function

$f(x)=-x^{2}-\frac{1}{x}+3x$ ,

we can plug in x=2 to get

$f(2)=-(2)^{2}-\frac{1}{(2)}+3(2)=-4-\frac{1}{2}+6=2-\frac{1}{2}=\frac{3}{2}$ .

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Example Question #75 : Algebraic Functions

Given a function $f(x)=3x^{2}-10+2x$ , what is f(1) ?

Possible Answers:

Correct answer:

Explanation:

Given a function

$f(x)=3x^{2}-10+2x$ ,

we can plug in x=1 to get

$f(1)=3(1)^{2}-10+2(1)=3-10+2=-7+2=-5$ .

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Example Question #71 : How To Find F(X)

Given a function $f(x)=\frac{3}4{x}+\frac{5}{3}$ , what is $f(\frac{4}{3})$ ?

Possible Answers:

$\frac{8}{5}$

$\frac{3}{8}$

$\frac{5}{}8$

$\frac{8}{3}$

$\frac{3}{5}$

Correct answer:

$\frac{8}{3}$

Explanation:

Given a function

$f(x)=\frac{3}4{x}+\frac{5}{3}$ ,

we can plug in $x=\frac{4}{3}$ to get

$f(\frac{4}{3})=\frac{3}4({\frac{4}{3}})+\frac{5}{3}=1+\frac{5}{3}=\frac{3}{3}+\frac{5}{3}=\frac{8}{3}$ .

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Example Question #77 : Algebraic Functions

Given a function $f(x)=x^{3}-\frac{1}{x^{2}}$ , what is f(2) ?

Possible Answers:

$\frac{33}{4}$

$\frac{30}{4}$

$\frac{32}{4}$

$\frac{29}{4}$

$\frac{31}{4}$

Correct answer:

$\frac{31}{4}$

Explanation:

Given a function

$f(x)=x^{3}-\frac{1}{x^{2}}$ ,

we can plug in x=2 to get

$f(2)=(2)^{3}-\frac{1}{(2)^{2}}=8-\frac{1}{4}=\frac{32}{4}-\frac{1}{4}=\frac{31}{4}$ .

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Example Question #78 : Algebraic Functions

Given a function $f(x)=2x^{2}-3x$ , what is f(10) ?

Possible Answers:

180

170

150

190

160

Correct answer:

170

Explanation:

Given a function

$f(x)=2x^{2}-3x$ ,

we can plug in x=10 to get

$f(10)=2(10)^{2}-3(10)=200-30=170$ .

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Example Question #79 : Algebraic Functions

Given a function $f(x)=x-(\frac{x^{2}-1}{3})$ , what is f(5) ?

Possible Answers:

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{5}{3}$

Correct answer:

Explanation:

Given a function

$f(x)=x-\left(\frac{x^{2}-1}{3}\right)$ ,

we can plug in x=5 to get

$f(5)=5-\left(\frac{(5)^{2}-1}{3}\right)=5-\frac{24}{3}=5-8=-3$

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Example Question #80 : Algebraic Functions

Given the function f(x) = 4x+6 , what is $f(\frac{2}{7})$ ?

Possible Answers:

$\frac{48}{7}$

$\frac{24}{7}$

$\frac{12}{7}$

$\frac{50}{7}$

Correct answer:

$\frac{50}{7}$

Explanation:

Start by replacing the number with the term in the function.

$f(\frac{2}{7}) = 4(\frac{2}{7})+6$

Simplify by distributing the four with the two in the numerator.

$4(\frac{2}{7})+6 = \frac{8}{7}+6$

Convert $\frac{6}{1}$ to $\frac{42}{7}$ and replace so that fractions with like denominators can be added.

$\frac{8}{7}+6 = \frac{8}{7}+ \frac{42}{7} = \frac{50}{7}$

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Example Question #81 : Algebraic Functions

f(z)=4z-10

and

$x\diamond y=x^{-y}$ ,

then what is the value of $f(5)\diamond 2$ ?

Possible Answers:

0.1

0.01

100

$\frac{1}{20}$

Correct answer:

0.01

Explanation:

This type of problem is very common on standardized tests, and examines a student's confidence level when dealing with unfamiliar material. Clearly, we don't learn how to "diamond" numbers in class! The diamond symbol, however, just represents some unknown operation. Here, to diamond two numbers simply means raising the first number to the negative second number. The solution is provided below:

First evaluate f(5). This simplifies to:

f(5)=4(5)-10=10 .

Now, we know that the question is asking for the value of:

$10\diamond 2=10^{-2}$ .

The rest of the solution is a simple matter of dealing with a negative exponent. Based on the laws of exponents, we know that

$10^{-2}=\frac{1}{10^2}=\frac{1}{100}=0.01$ .

Therefore, the answer to this question is 0.01.

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #71 : Algebraic Functions

Example Question #73 : Algebraic Functions

Example Question #74 : Algebraic Functions

Example Question #75 : Algebraic Functions

Example Question #71 : How To Find F(X)

Example Question #77 : Algebraic Functions

Example Question #78 : Algebraic Functions

Example Question #79 : Algebraic Functions

Example Question #80 : Algebraic Functions

Example Question #81 : Algebraic Functions

All Algebra 1 Resources

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