Algebra and Functions

The graph above shows the cost, in dollars, of apples as a function of the number of pounds of apples purchased at a particular grocery store. The equation above defines the cost C, in dollars, for p pounds of pears at the same store. Which of the following statements accurately compares the cost per pound of apples and the cost per pound of pears at this store?

• Apples cost approximately $0.07 less per pound than pears do.

• Apples cost approximately $0.04 less per pound than pears do.

• Apples cost approximately $0.73 less per pound than pears do.

• Apples cost approximately $0.62 more per pound than pears do.

Answer explanation

To compare costs, calculate the cost per pound for both apples and pears. The graph shows apples cost less per pound than the equation for pears. The difference is approximately $0.07, making A the correct choice.

Tags

CCSS.8.EE.B.5

Which of the following expressions is equivalent to 3x² + 6x – 24?

• 3(x + 2)(x – 4)

• 3(x – 2)(x + 4)

• (x + 6)(x – 12)

• (x – 6)(x + 12)

Answer explanation

To factor 3x² + 6x - 24, first factor out 3: 3(x² + 2x - 8). Then, factor the quadratic: (x - 2)(x + 4). Thus, the expression is 3(x - 2)(x + 4), which matches the correct choice.

x² + 5x – 9 = 5 Which of the following values of x satisfies the equation above

• 7

• 3

• 2

• -7

Answer explanation

To solve x^2 + 5x - 9 = 5, first simplify to x^2 + 5x - 14 = 0. Factoring gives (x + 7)(x - 2) = 0, leading to x = -7 or x = 2. The correct answer is -7.

Tags

CCSS.6.EE.B.5

The graph of y = f(x) is shown in the xy-plane. Which of the following equations could define f(x)?

• f(x) = x^2 – 2x – 8

• f(x) = –x^2 + 2x – 8

• f(x) = (x – 2)(x + 4)

• f(x) = –(x – 1)2 – 9

Answer explanation

The equation f(x) = x^2 – 2x – 8 is a quadratic function that opens upwards, matching the graph's shape. The other options either open downwards or do not fit the graph's characteristics.

Tags

CCSS.HSF-IF.C.7A

Is this graph a function or not a function? 

• Function 

• Not a Function 

If ( f(x) = x² + 3x + 1 , what is f(x + 2) ?

• x^2 + 3x + 3

• (x + 2)^2 + 3(x + 2) + 1

• (x + 2)(x^2 + 3x + 1)

• x^2 + 3x + 9

Answer explanation

To find f(x + 2), substitute x + 2 into f(x): f(x + 2) = (x + 2)^2 + 3(x + 2) + 1. This matches the correct answer choice, which expands to the function evaluated at x + 2.

Tags

CCSS.HSF.IF.A.2

Function g is defined by g(x) = 3(x + 8). What is the value of g(12)?

• A. -4

• B. 20

• C. 44

• D. 60

Answer explanation

To find g(12), substitute 12 into the function: g(12) = 3(12 + 8) = 3(20) = 60. Thus, the correct answer is D. 60.

Tags

CCSS.HSF.IF.A.2

Which of the following is an equation of the line that passes through the point (0, 0) and is perpendicular to the line shown above? Be cautious as it wants a perpendicular line which means the slopes are opposite reciprocals. Example: If slope is 2/3 perpendicular slope is -3/2 (One is always positive and one is always negative)

• y = 5/4 x

• y = 5/4 x + 3

• y = -4/5 x

• y = -4/5 x + 3

Answer explanation

The line perpendicular to another has a slope that is the negative reciprocal. If the original line has a slope of 4/5, the perpendicular slope is -5/4. The only equation that passes through (0,0) with this slope is A: y = 5/4 x.

Which of the following expressions is equivalent to (x + 7)(x² - 3x + 2)?

• A. x³ - 3x² + 2x + 14

• B. x³ + 4x² - 19x + 14

• C. x³ - 3x + 14

• D. x² - 2x + 9

Answer explanation

To find the equivalent expression, expand (x + 7)(x² - 3x + 2). This results in x³ + 4x² - 19x + 14, which matches choice B. The other options do not match the expanded form.

Tags

CCSS.HSA.APR.A.1

Which of the following is the graph of a function where y = f(x)?

• 
• 
• 
• 

Answer explanation

Choice C is correct. A function has one output for each input in its domain. Each x-value on this graph corresponds to only one y-value. Choices A, B, and D are incorrect because each has x-values that correspond to more than one y-value