MATH EXAM

Evaluate the expressions given functions f,g, and h: f(x)=3x-2 g(x)=5-x^2 h(x)=-2x^2+3x-1 a. 3f(1)-4g(-2) b. f(7/3)-h(-2)

a. -1 b. 20

f(x)=2x+15 and g(x)=x-15/2. Find the following composite functions. a. f(g(x)) b. g(f(x))

a. 1/2x+15/2 b. 1x

f(x)=x^2-2x-12, g(x)=-3x+2. Find the following composite function: f(g(x)).

9x^2-6x-12

a. 6-(3+2i)+(4-5i) b. (3-i)^2 - (1+i)^2

a. (7-7i) b. (8-8i)

State the degree of each of the following expression. a. (8x^5)(6x) b. 6x^3y^6z c. -52

a. 6 b. 10 c. 0

Find the indicated function given: g(x)=3x-5 a. g(f(x)) b.g(g(x))

a. 6x^2-2 b. 9x-20

Use long division to find the quotient and the remainder for the following. a. (x^2-5x+8)/(x-2) b. (x^3-8x^2+3x-11)/(x-3)

a. quotient: x-3; remainder: 2 b. quotient: x^2-5x-12; remainder: -47

Solve the quadratic equations by factoring. a. x^2-11x+18=0 b. 4x^2-49=0 c. 2x^2-14x+20

a. x=2; x=9 b. x=7/2; -7/2 c. x=2; x=5

solve the following linear equations for x. a. 3x-5=7 b. 2(x-7)-12=4(x-3)

a. x=4 b. x=-7

f(x)=-2x+6 and g(x)=x^2+5x-8. Use these functions to find each of the following functions. a. (f+g)(x) b. (f-g)(x)

a. x^2+3x-2 b. -x^2-7x+14

Find the equation of each line below. Write the answer in slope-intercept form. a. the line that passes through the points (-3,8) and (7,-4) b. the line with slope =-2 and passing through (4,-7)

a. y= -6/5 + 22/5 b. y=-2x+1

f(x)=2x^3+5x^2-7. Use the remainder theorem to evaluate f(-4).

f(-4)=-55

find the inverse for f(x)=-6x+11.

f(x)^-1=-x/6 + 11/6

Use the long division to divide. Specify the quotient and the remainder. (x^3-224)/(x-6)

quotient: x^2+6x+36; remainder: -8

write the complex conjugate of (-17-25i)

(-17+25i)

What are the possible rational roots for 2x^3-6x^2+3x+10=0. A factor of the equation is (x-5).

+1,-1,+2,-2,+5,-5,+10,-10,+5/2,-5/2,+10/2,-10/2

find the average rate of change of the function on the specified interval in the simplest terms of h. f(x)=x^2+3x+2 on [x,x+h].

2x+h+3

Use synthetic division to divide. (2x^3-6x^2-7x+3)/(x-4)

2x^2+2x+1+(7/(x-4))

Use long division to divide. (3x^2+23x+14)/(x+7)

3x+2

find the vertex for f(x)=-3x^2+18x-5 by using the formula to find the x-coordinate. Use this value to fin the y-coordinate. Write the formula that you will use.

x-coordinate: 3 y-coordinate: 22 vertex: (3,22)

for f(x)=(x-5)^2-9, find the following. a. vertex b. x-intercepts c. y-intercept

a. (5,-9) b. x=8; x=2 c. 16

Perform the indicated operations. a. (-12i+5i)+(21-4i) b. (14-11i)-(10+3i) c. (2-6i)(-3+8i)

a. (9+i) b. (4-14i) c. (42+34i)

f(x)=-2x^2-8x+2 a. f(5) b. f(-2) c. f(2x-3)

a. f(5)=-88 b. f(-2)=10 c. f(2x-3)=-8x^2+8x+8

Find functions f(x) and g(x) so the given functions can be expressed as h(x)=f(g(x)). a. h(x)=(x+2)^2

a. f(x)=x^2; g(x)=x+2

Determine if the function even, odd, neither: a. f(x)=x^3+3x b. f(s)=s^6+3s^2-20

a. odd b. even

Use synthetic division to find the quotient and the remainder for the following. a. (x^3+x^2+8x-5)/(x-4) b. (2x^4+4x^3+3x^2-8x+5)/(x-5)

a.quotient: x^2+5x+28; remainder: 107 b. quotient: 2x^3+14x^2+73x+357; remainder: 1790

find the slope of the line passing through the points (4,-9) and (-5,12)

slope(m)= -7/3

Find the x-intercepts of the polynomial function. C(t)=6t(t-4)^2(t+1)

t=0; t=4; t=-1

Find all roots of the equation x^3-6x^2+3x+10=0.

x= 5; x=-1; x=2

Solve for x: x^2+2x=-5

x=(-1+2i); x=(-1-2i)