Precalc Midterm

Find the product and write the result in standard form. 5i(3i-9)

15+45i

Divide and express the result in standard form. 4+5i/5-4i

i

Use synthetic division and the Remainder Theorem to find the indicated function value. F(x)=2x³-5x²-5x+8; f(-2)

-18

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. Log₇27

1.6937

For the given functions f and g, find the indicated composition. f(x)=8x²-2x, g(x) =18x-5 (f∘g)(8)

154,290

Evaluate the function at the given Val ue of the independent variable and simplify. f(x)=3x²-4x-3; f(x-1)

3x²-10x+4

Write the equation in its equivalent logarithmic form. ∛8=2

Log₈2= 1/3

Begin by graphing the standard quadratic function f(x)=x². Then use transformations of this graph to graph the given function. h(x) = -(x-2)²

Reflection across the x-axis Horizontal translation (right 2)

Use the given conditions to write an equation for the line in point-slope form. Passing through (7,2) and (4,3)

Y-2=-1/3(x-7) Y=-1/3x=13/3

Divide using synthetic division. X⁵+x³-2/x+3

x⁴-3x³+10x²-30x+90-(272/x+3)

Find the distance between the pair of points. (3, 3) and (-2,-4)

√74

Find the accumulated value of an investment of $1,200 at 8% compounded quarterly for 2 years.

$1,405.99

Find the accumulated value of an investment of $8,000 at 9% compounded continuously for 4 years.

$11,466.64

Use properties of logarithms to expand the logarithmic expression as much as possible. Log₄(x⁵/y⁸)

5log₄x-8log₄y

Write the equation in its equivalent exponential form. Log₆216=x

6˄x=216

Find the product and write the result in standard form. (9+8i)(5-5i)

85-5i

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 1/2 log₂x+log₂y

Log₂y√x

Begin by graphing the standard quadratic function f(x)=x². Then use transformations of this graph to graph the given function. h(x) = -(x-7)²+2

Reflection across the x-axis Horizontal translation (right 7) Vertical translation (up 2)

Solve the equation by expressing each side as a power of th same base and then equating exponents. 3˄(1+2x)=243

{2}

Solve the equation by expressing each side as a power of th same base and then equating exponents. 4˄(3x-7)=16

{3}

Use the Rational Zero Theorem to list all possible rational zeros for the given function. F(x)=7x³-x²+3

±1, ±1/7, ±3, ±3/7

Find the midpoint of the line segment whose end points are given. (2,1) and (4,4)

(3,5/2)

Find the x-intercepts (if any) for the graph of the quadratic function. F(x)=-x²+11x-30

(5,0), (6,0)

Find the midpoint of the line segment whose end points are given. (-8,-8) and(-4,-7)

(6,-7.5)

Evaluate the piecewise function at the given value of the independent variable. X²-5/x-3; If x≠3 G(x)= ;g(-3) X+1; if x=3

-2/3

Use the graph to find the indicated function value. Y=f(x). Find f(1)

-3.4

Solve the quadratic equation using the quadratic formula. Express the solution in standard form. 8x²+3x+3=0

-3±i√87/16

Divide using long division. (-20x³+26x²-13x+4)÷(5x-4)

-4x²+2x-1

For the given functions f and g, find the indicated composition. f(x)=5x + 10, g(x)=3x-1 (f∘g)(x)

15x+5

Evaluate the piecewise function at the given value of the independent variable. X+1 If x>-3 F(x)= ;f(-3) -(x+1); If x≤-3

2

Find and simplify the difference quotient f(x+h)-f(x)/h, h≠0 for the given function. F(x)=x²+6x+4

2x+h+6

Evaluate the expression without using a calculator. Log₇343

3

Solve the problem. Solve the equation 3x³-28x²+69x-20=0 given that 4 is a zero of f(x)=3x³-28x²+69x-20.

4, 1/3, 5

Perform the indicated operations and write the result in standard form. 3√-64 + 4√-49

52i