Mathematics Quiz: Functions and Graphs

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Questions and Answers

What are the range values of the function f(x)=-3x^2+5 for the domain values {-2, 0, 1}?

{-7, 2, 5}

Malik can spend no more than $24 to buy pecans and cashews. He will pay $6 per pound for pecans and $8 per pound for cashews. Which graph best represents the number of pounds of pecans and the number of pounds of cashews Malik can buy?

width cashews then length pecans

Which is closest to the slope of the line graphed above?

-3/2

Based on the scatter plot, which x value would best match y=12?

3 Signup and view all the answers

This relation is an inverse variation. {(-1,8),(4,-2),(-2,4)}. Which equation represents this relation?

y=-8/x Signup and view all the answers

Which is a solution to (2x+3)²=25?

-4 Signup and view all the answers

Which graph best represents the equation 4x+5y=-20?

bottom left corner Signup and view all the answers

Using the distance formula, d=rt, what is the value of t when d=3,520 and r=550?

6.4 Signup and view all the answers

Which equation is nearest to the line of best fit of the data in this scatterplot?

y=1/2x +1 Signup and view all the answers

Which is an equation of a line with a slope of 3 that passes through the origin?

y=3x Signup and view all the answers

The table gives the cost for different numbers of 100-sheet notebooks. The cost, C, varies directly as the number of notebooks, n. Which equation represents the relationship shown in the table?

C=2.15n Signup and view all the answers

Which is a zero of f(x)=x²−15x+54?

9 Signup and view all the answers

Which graph best represents the following inequality? y≤-1/3x+2

bottom half shaded line stopped at 2 Signup and view all the answers

When simplified, (2x²y³)⁴ equals -

16x⁸y¹² Signup and view all the answers

Which of the following equals 3x²−10x−8 when factored completely?

(3x+2)(x−4) Signup and view all the answers

Which is closest to the value of the slope of the line of best fit of the data in this scatterplot?

-1 Signup and view all the answers

What is the solution to the following equation? 3(x+5)−10=-2(x+10)

-5 Signup and view all the answers

Karen makes $5 per hour babysitting and $12 per hour giving music lessons. One weekend, she worked a total of 18 hours and made $139. How many hours did she spend babysitting?

11 Signup and view all the answers

The continent of North America has an area of approximately 9.4 × 10^6 square miles. The area of Asia is approximately 1.74 × 10^7 square miles. How many square miles larger is Asia than North America?

8.0 × 10^6 Signup and view all the answers

Which is equivalent to b⁶/b²?

b⁴ Signup and view all the answers

Which number is a zero of the function h? h(x)=x²+3x−18

-6 Signup and view all the answers

What value of p will make this equation true? 6p+46=4p−83

10 Signup and view all the answers

Which is equivalent to the following expression? (-2xy)³

-8x³y³ Signup and view all the answers

What is the solution of the system of equations shown? {2x+5y=8, 6x+4y=-20}

(-6, 4) Signup and view all the answers

Which ordered pair represents the solution to the system of equations? {2x−7y=0, x−6y=-5}

(7, 2) Signup and view all the answers

Which graph best represents the line y=1/3x−2?

across the whole bottom Signup and view all the answers

Which of the following is most likely a graph of y=-2x+3?

arrow pointing towards the left across the whole graph Signup and view all the answers

Which graph best represents the function y=4x+2?

in the middle of the graph slightly to the right Signup and view all the answers

Which line has a y-intercept of -3 and an x-intercept of 2?

pointing towards the right on the two Signup and view all the answers

Which of the following sets of ordered pairs is a function?

{(1, 1), (2, 1), (3, 2), (4, 4)} Signup and view all the answers

What is the range of the function of x graphed above?

{all real numbers between -5 and 3} Signup and view all the answers

Which of the following is most likely the graph of a line with a slope of zero?

across on the 3 Signup and view all the answers

What is the solution to the following system of linear equations? {4x−y=-6, x−2y=-5}

(-1, 2) Signup and view all the answers

What are the x- and y-intercepts of the line with equation 4x+5y=40?

x-intercept 10, y-intercept 8 Signup and view all the answers

A data set with an even number of data points is ordered from least to greatest. The middle two data points are represented by x1, and x2. This formula can be used to find the median of the data set. m=x1+x2/2. Which shows this formula solved for x1?

x1=2m−x2 Signup and view all the answers

If f(x)=7(x−2)+4(x+1), what is f(2)?

12 Signup and view all the answers

Which is an equation for the line that passes through the origin and has a slope of 3/5?

y=3/5x Signup and view all the answers

Which is an example of the commutative property of addition?

3+5m=5m+3 Signup and view all the answers

Which equation is the slope-intercept form of -x+6y=12?

y=16x+2 Signup and view all the answers

Study Notes

Function and Range

The function f(x)=-3x^2+5 yields range values of {-7, 2, 5} for domain values {-2, 0, 1}.

Cost Constraints

Malik’s budget for pecans and cashews is $24, paying $6 per pound for pecans and $8 per pound for cashews.

Slope Characteristics

The slope of a specified line graph is approximately -3/2.
The slope of the line of best fit in a given scatterplot is estimated at -1.

Scatter Plot Analysis

The best x value that corresponds to y=12 in the scatter plot is 3.

Inverse Variation

The inverse relation defined by the points {(-1,8),(4,-2),(-2,4)} is represented by the equation y=-8/x.

Solving Equations

A solution to the equation (2x+3)²=25 is -4.
The solution for the equation 3(x+5)−10=-2(x+10) is -5.

Graphical Representation

The graph corresponding to the equation 4x+5y=-20 is located in the bottom left corner.
The inequality y≤-1/3x+2 is represented by a graph with the bottom half shaded and stopping at 2.

Mathematical Expressions

When simplified, (2x²y³)⁴ equals 16x⁸y¹².
Factoring 3x²−10x−8 results in (3x+2)(x−4).

Function Zeros

The zero of the function f(x)=x²−15x+54 is 9.
h(x)=x²+3x−18 has a zero at -6.

Equation Solutions

The cost equation for 100-sheet notebooks varies directly according to C=2.15n.
The value of p that satisfies the equation 6p+46=4p−83 is 10.

Coordinate Representation

The solution for the system of equations {2x+5y=8, 6x+4y=-20} is (-6, 4).
The ordered pair (7, 2) represents the solution for the system of equations {2x−7y=0, x−6y=-5}.

Graph Characteristics

The line represented by y=1/3x−2 runs across the entire bottom of the graph.
The graph of y=-2x+3 points towards the left across the entire graph.

Function Range and Zones

The function range is identified as all real numbers between -5 and 3.
The x-intercept and y-intercept of the line 4x+5y=40 are 10 and 8, respectively.

Median Calculation

The median of a data set can be found using the formula m=(x₁+x₂)/2 which solves to x₁=2m−x₂.

Calculating Function Values

Evaluating f(2) for f(x)=7(x−2)+4(x+1) results in 12.

Slope-Intercept Form

An equation representing a line with a slope of 3/5 passing through the origin is y=3/5x.
The slope-intercept form of -x+6y=12 is y=16x+2.

Commutative Property Example

The equation 3+5m=5m+3 exemplifies the commutative property of addition.

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Description

Test your understanding of range values of quadratic functions and budget constraints in purchasing items. This quiz covers key concepts including range calculations and graphical representation of inequalities. Ideal for students studying algebra and functions.