Math Midterm

Begin by graphing the standard absolute value function f(x) =x. Then use transformations of this graph to graph the given function. 38) g(x) = 1/4 |x - 6| - 5 A) B) C) D)

A)

Begin by graphing the standard square root function f(x) =x . Then use transformations of this graph to graph the given function. 37) g(x) = - (√x + 2) + 2 A) B) C) D)

A)

Identify the intervals where the function is changing as requested. 29) Increasing A) (-2, 2) B) (-2, ∞) C) (-3, 3) D) (-3, ∞)

A) (-2, 2)

13) -8x ≥ 48 A) (-∞, -6] B) (-∞, 6] C) [6, ∞) D) [-6, ∞)

A) (-∞, -6]

Find the slope of the line that goes through the given points. 30) (5, 1), (-1, 3) A) -1/3 B) 1/3 C) - 3 D)

A) -1/3

Given functions f and g, perform the indicated operations. 39) f(x) = 4x - 7, g(x) = 8x - 2 Find f - g. A) -4x - 5 B) -4x - 9 C) 4x + 5 D) 12x - 9

A) -4x - 5

Determine whether the relation is a function. 19) {(-3, 6), (-2, -6), (3, -2), (3, -9)} A) Not a function B) Function

A) Not a function

Use the graph to determine the function's domain and range. A) domain: [0, ∞) range: [, ∞) B) domain: [0, ∞) range: (-∞, ∞) C) domain: [0, ∞) range: [0, ∞) D) domain: (-∞, Q) range: [, ∞)

A) domain: [0, ∞) range: [2, ∞)

Find the inverse of the one-to-one function. 45) f(x) = 2x + 3/5 A) f^-1(x) = (5x - 3)/2 B) f^-1(x) = 5/(2x - 3) C) f^-1(x) = 5/(2x + 3) D) f^-1(x) = (5x + 3)/2

A) f^-1(x) = (5x - 3)/2

Find the inverse of the one-to-one function. 46) f(x) = (^3√3x + 8) A) f^-1(x) = x^3 - 8 B) f^-1(x) = x^3 + 64 C) f^-1(x) = 1/(x^3 - 8) D) f^-1(x) = x - 8

A) f^-1(x) = x^3 - 8

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. A) function B) not a function

A) function

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. A) not a function B) function

A) not a function

Evaluate the function at the given value of the independent variable and simplify. 27) f(x) = x^2- 1 ; f(x - 4) A) x^2 - 8x + 15 B) x^2 + 16 C) x^2 - 5 D) x^2 - 8x + 16

A) x^2 - 8x + 15

Use the given conditions to write an equation for the line in point-slope form. 31) Slope = -2, passing through (2, 6) A) y - 6 = -2(x - 2) B) x - 6 = -2(y - 2) C) y = -2x + 10 D) y + 6 = -2(x + 2)

A) y - 6= -2(x - 2)

Use the given conditions to write an equation for the line in slope-intercept form. 33) Passing through (8, 8) and (6, 2) A) y = x - 16 B) y = - 3x - 16 C) y = mx - 16 D) y - 8 = (x - 8)

A) y = x - 16

Determine whether the equation defines y as a function of x. 20) x^2 + y = 81 A) y is a function of x B) y is not a function of x

A) y is a function of x

10) 5x^2+ 12x = - 3 A) {-6 - √21/5 , -6 + √21/5} B) {-12 - √21/5 , -12 + √21/5} C) {-6 - √51/5 , -6 + √51/5} D) {-6 - √21/10 , -6 + √21/10}

A) {-6 - √21/5 , -6 + √21/5}

9) 5x^2 = 35 A){-√7, √7} B){8} C){17.5} D){-7, 7}

A) {-√7, √7}

Solve the problem. 4)You inherit $42,000 from a very wealthy grandparent, with the stipulation that for the first year, the money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $2400? A)$30,000 invested at 4%; $12,000 invested at 10% B)$22,000 invested at 4%; $20,000 invested at 10% C)$12,000 invested at 4%; $30,000 invested at 10% D)$20,000 invested at 4%; $22,000 invested at 10%

A)$30,000 invested at 4%; $12,000 invested at 10%

Begin by graphing the standard quadratic function f(x) =x2 . Then use transformations of this graph to graph the given function. 36) h(x) = (x - 2)^2 + 4 A) B) C) D)

B)

14) 2x + 10 < 20 A) (-∞, 5] B) (-∞, 5) C) [5, ∞) D) (5, ∞)

B) (-∞, 5)

3) Solve the equation. (x/2x + 2) = (-2x/4x + 4) + (2x - 3/x + 1) A) -3 B) 3 C) 3/2 D) -12/5

B) 3

For the given functions f and g , find the indicated composition. 42) f(x) = 8x + 12 , g(x) = 4x - 1 (f(g)(x) A) 32x + 20 B) 32x + 4 C) 32x + 11 D) 32x + 47

B) 32x + 4

Does the graph represent a function that has an inverse function? 44) A) Yes B) No

B) No

15) {(-8, -1), (-5, 3), (-4, -6), (5, -5)} A) domain = {-4, -5, -8, 5}; range = {-6, -6, 3, -1, -5} B) domain = {-4, -5, -8, 5}; range = {-6, 3, -1, -5} C) domain = {-6, 3, -1, -5}; range = {-4, -5, -8, 5} D) domain = {-4, -5, -8, 5}; range = {-6, 1, 3, -1, -5}

B) domain = {-4, -5, -8, 5}; range = {-6, 3, -1, -5}

Use the graph to determine the function's domain and range. A) domain: (-∞, ∞) range: (-∞, ∞) B) domain: (-∞, ∞) range: (-∞, 2] C) domain: (-∞, 5] range: (-∞, 2] D) domain: (-∞, 5) or (5, ∞) range: (-∞, 2) or (2, ∞)

B) domain: (-∞, ∞) range: (-∞, 2]

Use the given conditions to write an equation for the line in the indicated form. 34)Passing through (5, -2) and parallel to the line whose equation is y = -4x +4 ; slope-intercept form A) y = -1/4x - 9/2 B) y = - 4x + 18 C) y = - 4x - 18 D) y = 4x - 18

B) y = - 4x + 18

Use the given conditions to write an equation for the line in the indicated form. 35) Passing through (2, 2) and perpendicular to the line whose equation is y = 1/9x + 5 ; slope-intercept form A) y = -19x - 209 B) y = - 9x + 20 C) y = - 9x - 20 D) y = 9x - 20

B) y = - 9x + 20

Use the given conditions to write an equation for the line in slope-intercept form. 32) Slope = -3, passing through (-3, 3) A) y = -3x + 6 B) y = -3x - 6 C) y - 3 = -3x + 3 D) y - 3 = x + 3

B) y = -3x - 6

11) 5x - 4 = 80x^3-64x^2 A) {-1/16, 1/16, 4/5} B) {-1/4, 1/4, 4/5} C) {0, 4/5} D) {-1/4, 1/4, 5/4}

B) {-1/4, 1/4, 4/5}

Determine whether the equation defines y as a function of x. 23) x + y^2 = 25 A) y is a function of x B) y is not a function of x

B)y is not a function of x

Find the domain of the function. 18) f(x) =x - 4 A) (0, ∞) B) [4, ∞) C) (-∞, ∞) D) (-∞, 0) u (0, ∞)

C) (-∞, ∞)

22)x/(√x - 6) A) (-∞, 6) U (6, ∞) B) (-∞, ∞) C) (6, ∞) D) [6, ∞)

C) (6, ∞)

Evaluate the piecewise function at the given value of the independent variable. 28) f(x) = 2x - 1 if x < -4 -4x - 3 if x ≥ -4 Determine f(-7). A) -14 B) C) -15 D) -18

C) -15

Solve and check the linear equation A){} B){} C){- 16} D){0}

C) {-16}

12)x^3 + 2x^2 - 24x = 0 A){6, -4} B){0, 6, -4} C){0, -6, 4} D){-6, 4}

C) {0, -6, 4}

7) 5x2- 11x = 0 A) {-11/5, 0} B){0} C){0, 11/5} D) {11/5, -11/5}

C) {0, 11/5}

Find the domain of the function. 21) g(x) = 2x/ x^2 - 64 A) (-∞, ∞) B) (-∞, 0) U (0, ∞) C) (64, ∞) D) (-∞, -8) U (-8, 8) U (8, ∞)

D) (-∞, -8) U (-8, 8) U (8, ∞)

Evaluate the function at the given value of the independent variable and simplify. 26) f(x) = x + 4 ; f(-3) A) B) -31 C) -39 D) -23

D) -23

For the given functions f and g , find the indicated composition. 43) f(x) = -6x + 4 , g(x) = 5x + 9 (g(f)(x) A) 30x + 29 B) -30x - 11 C) -30x + 58 D) -30x + 29

D) -30x + 29

Given functions f and g, perform the indicated operations. 40) f(x) = 9 - 6x , g(x) = -2x + 6 Find f + g. A) 7x B) -2x + 9 C) -4x + 15 D) -8x + 15

D) -8x + 15

41) f(x) = 3x - 8 , g(x) = 8x - 5 Find fg. A) 11x^2 - 79x - 13 B) 24x^2 - 69x + 40 C) 24x^2 + 40 D) 24x^2 - 79x + 40

D) 24x^2 - 79x + 40

2) Solve the equation. (x/5) = (x/6) +(6/5) A)-6/5 B)0 C)1/36 D)36

D) 36

5) The length of a rectangular room is 8 feet longer than twice the width. If the room's perimeter is172 feet, what are the room's dimensions? A)Width =31 ft; length =70 ft B)Width =39 ft; length =47 ft C)Width =52 ft; length =120 ft D)Width =26 ft; length =60 ft

D) Width =26 ft; length =60 ft

8) (2x - 5)^2 = 121 A){-16, 6} B){-8, 3} C){-6, 16} D){-3, 8}

D) {-3, 8}

Solve the equation by factoring. 6) x2 + 7x - 60= 0 A){12, -5} B){-12, 1} C){12, 5} D){-12, 5}

D){-12, 5}