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Algebra 1 : Algebraic Functions

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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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Example Question #3411 : Algebra 1

f(x) = -3x+5

find f(-4) .

Possible Answers:

f(-4) = -7

f(-4) = -4

f(-4) = 8

f(-4) = 17

f(-4) = 12

Correct answer:

f(-4) = 17

Explanation:

Given

f(x) = -3x+5

we must find f(-4) .

All we do is substitute -4 for the variable x.

So anywhere we see x, we will change to -4.

We get

$f(-4) = (-3 \cdot -4) + 5$

f(-4) = 12 + 5

f(-4) = 17

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Example Question #83 : Algebraic Functions

Find f(-2) if

f(x) = 4x^2 - 3x +9 .

Possible Answers:

f(-2) = -1

f(-2) = 31

f(-2) = 19

f(-2) = -13

f(-2) = 23

Correct answer:

f(-2) = 31

Explanation:

Given f(-2) , when solving

f(x) = 4x^2 - 3x +9

we simply substitute.

In this case x = -2 . So anywhere we see an x, we will substitute -2. So,

f(x) = 4x^2 - 3x +9

f(-2) = 4(-2)^2 - 3(-2) + 9

$f(-2) = 4 \cdot 4 + 6 + 9$

f(-2) = 16 + 6 + 9

f(-2) = 31

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Example Question #81 : Algebraic Functions

If x = -4 , solve

f(x) = 2x^2 - 4

Possible Answers:

f(-4) = -28

f(-4) = 60

f(-4) = -36

f(-4) = -68

f(-4) = 28

Correct answer:

f(-4) = 28

Explanation:

When solving a function, we simply substitute the value into the equation. So, we know x = -4 . So in the function

f(x) = 2x^2 - 4

we substitute -4 in for x. By doing that, we get

f(-4) = 2(-4)^2 - 4

We now solve using the order of operations. We get

$f(-4) = 2 \cdot 16 - 4$

f(-4) = 32 - 4

f(-4) = 28

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Example Question #81 : How To Find F(X)

If x = -3 , solve

f(x) = 3x^2 -5x + 1

Possible Answers:

f(-3) = 43

f(-3) = -32

f(-3) = -41

f(-3) = -12

f(-3) = 34

Correct answer:

f(-3) = 43

Explanation:

To solve a function, we simply substitute the value of x into the equation. So, given that

x = -3

we will substitute into the function.

f(x) = 3x^2 -5x + 1

f(-3) = 3(-3)^2-5(-3)+1

f(-3) = 3(9) -5(-3)+1

f(-3) = 27 + 15 + 1

f(-3) = 43

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Example Question #86 : How To Find F(X)

If x = -4 , then solve

f(x) = -2x^2 - 5x + 1

Possible Answers:

f(-4) = -13

f(-4) = 13

f(-4) = -11

f(-4) = -51

f(-4) = 53

Correct answer:

f(-4) = -11

Explanation:

We know x = -4 . When solving a function, we substitute the value of x into the function. In other words, anywhere we see an x, we will replace it with -4.

f(x) = -2x^2 - 5x+1

f(-4) = -2(-4)^2-5(-4)+1

f(-4) = -2(16)+20+1

f(-4) = -32+20+1

f(-4) = -11

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Example Question #131 : Functions And Lines

If x = 3 , then solve

f(x) = -2x^2+2x-4

Possible Answers:

f(3) = -16

f(3) = 20

f(3) = 28

f(3) = -8

f(3) = -10

Correct answer:

f(3) = -16

Explanation:

We know x=3 . When solving a function, we substitute the value of x into the function. In other words, anywhere we see an x, we will replace it with 3.

f(x) = -2x^2+2x-4

f(3) = -2(3)^2+2(3)-4

f(3) = -2(9)+6-4

f(3) = -18+6-4

f(3) = -16

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Example Question #81 : Algebraic Functions

Given the following zeros, write out the polynomial function, but don't expand:

x=2, -3, 4

Possible Answers:

(x-2)(x+3)(x-4)=0

(x-2)(x-3)(x-4)=0

(x+2)(x-3)(x+4)=0

Correct answer:

(x-2)(x+3)(x-4)=0

Explanation:

To find the polynomial function given the zeros of the function, we must work backwards. If we know that each zero came from a term that was set equal to x, and this term was either added or subtracted to x, we can simply flip the sign on all of the zeros to get the polynomial function they came from:

(x-2)(x+3)(x-4)=0

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Example Question #83 : How To Find F(X)

If x = -9 , solve the following function:

f(x) = -3x^2 - 5x + 8

Possible Answers:

f(-9) = -190

f(-9) = 296

f(-9) = 107

f(-9) = -280

f(-9) = -1

Correct answer:

f(-9) = -190

Explanation:

When solving a function, we substitute the value of x into the function itself. So, we know that x = -9 . We will substitute this value into the given function.

f(x) = -3x^2 - 5x + 8

f(-9) = -3(-9)^2-5(-9)+8

f(-9) = -3(81)+45+8

f(-9) = -243+45+8

f(-9) = -190

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Example Question #82 : How To Find F(X)

If x = 6 , solve the following function:

f(x) = -2x^2-3x-8

Possible Answers:

f(6) = -50

f(6) = -98

f(6) = -14

f(6) = 14

f(6) = -62

Correct answer:

f(6) = -98

Explanation:

When solving a function, we will substitute the value of x into the function itself. We know that x = 6 , so we will substitute 6 into the function wherever we see the variable x. So,

f(x) = -2x^2-3x-8

f(6) = -2(6)^2-3(6)-8

f(6) = -2(36) - 18 - 8

f(6) = -72 - 18 - 8

f(6) = -98

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Algebra 1 : Algebraic Functions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Algebraic Functions

Example Question #3411 : Algebra 1

Example Question #83 : Algebraic Functions

Example Question #81 : Algebraic Functions

Example Question #81 : How To Find F(X)

Example Question #86 : How To Find F(X)

Example Question #131 : Functions And Lines

Example Question #81 : Algebraic Functions

Example Question #83 : How To Find F(X)

Example Question #82 : How To Find F(X)

All Algebra 1 Resources

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