Chapter 1 Practice Test 2020 - Multiple Choice and Short Answer Questions

Q: How do you determine whether a relation is a function?

Check whether each input x in the set corresponds to exactly one output y. If any x is paired with more than one y, it is not a function.

Q: What do you need to find when evaluating a function at a given value?

Substitute the independent variable with the given value into the function and simplify the resulting expression to get the output.

Q: How are inverse functions and inverse graphs handled in the test?

You determine whether the graph represents a function with an inverse, find the inverse of a one-to-one function, and graph f⁻1 given f(x), then state the domain and range of f⁻1 using interval notation.

Sep 30, 2026

Upload by Mafia Boss

Chapter 1 practice test 2020 focused on functions and graph-based analysis. It includes multiple-choice and short-answer items that test whether relations are functions, evaluate functions and piecewise functions at given values, identify increasing intervals, determine domain and range from graphs, and find relative maxima and minima. Students also classify functions as even, odd, or neither, work with inverse functions and inverse composition, compute difference quotients, derive line equations, perform function operations (sum, product), compositions, and solve a ticket-price revenue model.

LanguageEnglish

CategoryExam

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Multiple Choice

Determine functions and function properties

Solve function evaluation and interval questions

Inverse functions and graph-based analysis

Short Answer

Function evaluation and simplification

Domain, range, and relative extrema

Even/odd classification and inverse computations

Compositions, difference quotient, and line equations

Piecewise and airline revenue word problem

Chapter 1 Practice Test 2020 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the relation is a function. 1) {(-9, -7), (-9, 5),(1, 2),(5, -2),(10, -2)} 1) A) Function B) Not a function 2) x2 + y2 = 25 2) A) Function B) Not a function 3) y = - x + 1 3) A) Function B) Not a function SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the function at the given value of the independent variable and simplify. 4) f(x) = 3x2 + 2x-3; f(x-1) 4) x3 + 8 5) f(x) = ; f(2) 5) x2-8 Identify the intervals where the function is changing as requested. 6) Increasing 6) Use the graph to determine the functionʹs domain and range. 7) Use the graph of the given function to find the point(s) of any relative maxima and relative minima. 8) f(x) = x3-12x + 2 7) 8) Determine whether the given function is even, odd, or neither. 9) f(x) = 5x2 + x4 9) 10) f(x) = x3 + x2 + 1 10) Evaluate the piecewise function at the given value of the independent variable. 11) f(x) =x + 5 if x > 1 ; f(-3) 11) -(x + 5) if x ≤ 1 x2 + 4 if x ≠ 3 12) h(x) = x-3 ; h(3) 12) x-1 if x = 3 Graph the function. 13) f(x) = x-1 if x < 1 13) -5 if x ≥ 1 y 5 -5 5 x -5 Find and simplify the difference quotient ~~ f(x ~~+~~ hh~~)~~ ~~-~~f(x) ~~, h ≠ 0 for the given function. 14) f(x) = x2 + 7x + 5 14) Use the given conditions to write an equation for the line in slope-intercept form. 15) Passing through (1, -4) with x-intercept = -1 Use the given conditions to write an equation for the line in point-slope form. 16) Passing through (8, -7) and (-4, -1) Given functions f and g, perform the indicated operations. 17) f(x) = 3-3x, g(x) = -8x + 3 Find f + g. 18) f(x) = 3x2-8x, g(x) = x2-5x-24 Find ~~ ~~fg~~ ~~ . For the given functions f and g , find the indicated composition. 19) f(x) = 8x2-5x, g(x) = 12x-9 (f∘g)(11) 15) 16) 17) 18) 19) | | | --- | | | | | | | MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find functions f and g so that h(x) = (f ∘ g)(x). 6 20) h(x) = 20) 2x + 9 A) f(x) = 2x + 9, g(x) = 6 B) f(x) = 6/x, g(x) = 2x + 9 C) f(x) = 6, g(x) = 2 + 9 D) f(x) = 6/ x, g(x) = 2x + 9 Determine which two functions are inverses of each other. 21) f(x) = x~~ ~~+2~~ ~~3~~ ~~ g(x) = 2x + 3 h(x) = x~~ ~~2-3~~ ~~ 21) A) f(x) and h(x) B) g(x) and h(x) C) f(x) and g(x) D) None SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the inverse of the one-to-one function. 7x + 8 22) f(x) = 22) 5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Does the graph represent a function that has an inverse function? 23) 23) y x A) No B) Yes SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph f-1 given f(x) in the rectangular coordinate space. Use interval notation to give the domain and range of f-1. 24) f(x) = x2-6, x ≥ 0 For the given functions f and g , find the indicated composition. 25) f(x) = 4x2 + 2x + 8, g(x) = 2x-3 (g∘f)(x) 24) 25) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 26) On a certain route, an airline carries 6000 passengers per month, each paying $100. A market 26) survey indicates that for each $1 decrease in the ticket price, the airline will gain 40 passengers. a. Express the number of passengers per month, N, as a function of the ticket price, x. b. Express the monthly revenue for the route, R, as a function of the ticket price, x. A) a. N(x) = 40x + 2000 B) a. N(x) = -40x + 2000 b. R(x) = 40x2 + 2000x b. R(x) = -40x2 + 2000x C) a. N(x) = 40x + 10,000 D)

FAQs

How do you determine whether a relation is a function?

Check whether each input x in the set corresponds to exactly one output y. If any x is paired with more than one y, it is not a function.

What do you need to find when evaluating a function at a given value?

Substitute the independent variable with the given value into the function and simplify the resulting expression to get the output.

How are inverse functions and inverse graphs handled in the test?

You determine whether the graph represents a function with an inverse, find the inverse of a one-to-one function, and graph f⁻1 given f(x), then state the domain and range of f⁻1 using interval notation.

Sep 30, 2026

Upload by Mafia Boss