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
