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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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

Example Questions

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 : How To Find F(X)

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 #90 : How To Find F(X)

If x = 6 , solve the following function:

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

Possible Answers:

f(6) = -14

f(6) = -98

f(6) = -62

f(6) = 14

f(6) = -50

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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Example Question #3 : Understand Functions: Ccss.Math.Content.8.F.A.1

Define $f(x) = x^{2} - 4x + 7$ .

Evaluate f(6) .

Possible Answers:

f(6) = 5

f(6) = -132

f(6) = 19

f(6) = 199

f(6) = 121

Correct answer:

f(6) = 19

Explanation:

To evaluate f(6) substitute six in for every x in the equation.

$f(x) = x^{2} - 4x + 7$

$\\f(6) = 6^{2} - 4 \cdot 6 + 7 \\f(6)= 36 - 24 + 7\\f(6) = 12 + 7 \\f(6)= 19$

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Example Question #4 : Understand Functions: Ccss.Math.Content.8.F.A.1

Define g(x )= 3x - 13

Which of the following is equivalent to g(x+ 6 ) ?

Possible Answers:

3x-5

3x+ 7

3x- 7

3x+ 5

Correct answer:

3x+ 5

Explanation:

To solve this problem replace every x in g(x) with x+6 .

g(x )= 3x - 13

Therefore,

g(x+ 6 )= 3(x+ 6 ) - 13

$= 3\cdot x+ 3 \cdot 6 - 13$

= 3 x+ 18- 13

= 3 x+ 5

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Example Question #91 : How To Find F(X)

If f(x) = 7x-6 , solve for f(x) if $f(\frac{1}{7})$ .

Possible Answers:

$-\frac{6}{7}$

$-7\frac{1}{6}$

$7\frac{1}{6}$

Correct answer:

Explanation:

We are given an equation that is a function of x. Substitute the given fraction and replace it with the variable.

$f(\frac{1}{7}) = 7(\frac{1}{7})-6$

Simplify the right side.

$7(\frac{1}{7})-6 = 1-6 = -5$

The answer is:

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Example Question #2 : Finding Roots

Solve the equation:

$\small 13 = x^2-12x$

Possible Answers:

$\small \left \{-1, 13 \right \}$

$\small \left \{0\right\}$

$\small \left \{ 2, 4\right \}$

$\small \left \{ 1, 2 \right \}$

$\small \left \{-13, 1\right \}$

Correct answer:

$\small \left \{-1, 13 \right \}$

Explanation:

To solve the quadratic equation, $\small 13= x^{2} -12x$ , we set the equation equal to zero and then factor the quadratic, $\small (x-13)(x+1)=0$ . Because these expressions multiply to equal 0, then it must be that at least one of the expressions equals 0. So we set up the corresponding equations x-13=0 and x+1=0 to obtain the answers x=13 and x=-1 .

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Example Question #3422 : Algebra 1

Solve for :

$x^{2}+12x+35=0$

Possible Answers:

x=3,15

x=7,9

x=-5,-7

The solution is undefined.

x=-5,-9

Correct answer:

x=-5,-7

Explanation:

To factor this equation, first find two numbers that multiply to 35 and sum to 12. These numbers are 5 and 7. Split up 12x using these two coefficients:

x^2 + 7x+5x+35=0

x(x+7)+5(x+7)=0

(x+5)(x+7)=0

x=-5,-7

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Example Question #3423 : Algebra 1

Given $f(x) = -2x^{2} - 3x +5$ , find f(a+h) - f(a) .

Possible Answers:

$4ah+2h^{2} -3h$

$2a^{2}+3a-5$

f(a+h) -f(a)

$-2a^{2}-4ah-2h^{2} -3a -3h +5$

$-2h^{2} - 4ah -3h$

Correct answer:

$-2h^{2} - 4ah -3h$

Explanation:

Plug in a for x:

$f(a)=-(-2a^{2}-3a+5) = 2a^2+3a-5$

Next plug in (a + h) for x:

$f(a+h) = -2(a+h)^2-3(a+h)+5 = -2a^{2} - 4ah - 2h^{2} -3a - 3h +5$

Therefore f(a+h) - f(a) = $-2h^{2} - 4ah - 3h$ .

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #131 : Functions And Lines

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

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

Example Question #90 : How To Find F(X)

Example Question #3 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #4 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #91 : How To Find F(X)

Example Question #2 : Finding Roots

Example Question #3422 : Algebra 1

Example Question #3423 : Algebra 1

All Algebra 1 Resources

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