PreCalculus Quiz: Graphing Functions, Function Composition, and Area of a Right Triangle, Exercises of Calculus

A honors precalculus quiz covering topics such as graphing functions, finding function composites, and calculating the area of a right triangle. The quiz includes short answer and multiple choice questions related to functions like x^3 + 2, |x + 2| + 2, and their transformations. Students are required to find the equations of shifted functions, find the sum, difference, product, and quotient of functions, and determine the domain of a composite function.

Typology: Exercises

2012/2013

Uploaded on 02/06/2013

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Honors PreCalculus Quiz 2.1-2.7 & A8 Name__________________________________
_
SHORT ANSWER. SHOW ALL WORK!
Graph the function. Remember to have the graph contain 3 points
1
)
f(x) = x3 + 2
x
-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x
-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
2
)
Graph:
f
(x) = |x + 2| + 2
x
-10 10
y
10
-10
x
-10 10
y
10
-10
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question
.
Solve the problem.
3
)
The graph of y = x2 is shifted to the right by 3 units. Write the resulting equation.
A) y = (x + 3)2B) y = 3x2C) y = (x - 3)2D) y = x2 + 3
SHORT ANSWER. SHOW ALL WORK!
Find the requested function.
4
)
Given the functions f(x) = x - 2 and g(x) = 3x - 3, find (f + g)(x), (f - g)(x), (f œg)(x), and (f/g)(x).
1
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Honors PreCalculus Quiz 2.1-2.7 & A8 Name___________________________________

SHORT ANSWER. SHOW ALL WORK! Graph the function. (^) Remember to have the graph contain 3 points

  1. f(x) = x3 + 2

-6 -4 -2 2 4 6 x

6 y 4 2

-6 -4 -2 2 4 6 x

6 y 4 2

  1. Graph: f ( x ) = | x + 2| + 2

-10 10 x

10 y

-10 10 x

10 y

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem.

  1. The graph of y = x2 is shifted to the right by 3 units. Write the resulting equation. A) y = (x + 3)2^ B) y = 3x2^ C) y = (x - 3)2^ D) y = x2 + 3

SHORT ANSWER. SHOW ALL WORK!

Find the requested function.

  1. Given the functions f ( x ) = x - 2 and g ( x ) = 3 x - 3, find ( f + g )( x ), ( f - g )( x ), ( f (^) œ g )( x ), and ( f / g )( x ).

Find the indicated composite for the pair of functions.

  1. (f † g)(x): f(x) = (^) x - 6^7 , g(x) = (^) 7x^8

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

  1. (g (^) † f)(x): f(x) = 4x2 + 5x + 3, g(x) = 5x - 5 A) 20x2 + 25x + 10 B) 4x2 + 25x + 10 C) 20x2 + 25x + 20 D) 4x2 + 5x - 2

SHORT ANSWER. SHOW ALL WORK!

Solve the problem.

  1. Let f(x) = 2 - x and g(x) = 2x - 1. Find the domain of (f † g)(x). Express answer in interval notation.

Find the domain of the composite function f (^) † g.

  1. f(x) = x - 1; g(x) = (^) x - 6^1

Solve the problem.

  1. A right triangle has one vertex on the graph of y = x at ( x , y ), another at the origin, and the third on the (positive) y -axis at (0, y ). Express the area A of the triangle as a function of x.