Introduction to Precalculus and Polynomial Functions - Part 1

What is the domain of the function? f(x)=x−2/2x^2+x−10

(−∞−5/2)∪(−5/2,2)∪(2,∞)

What are the roots of the equation? 0=x4−3x3+8x2−18x+12 Select all correct answers.

1 2 i√6 -i√6

What two rational expressions sum to 4x+1/x^2−4x−12? Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.

4x+1/x^2−4x−12+ 25/8(x-6) + 7/8(x+2)

Andrew needs to determine whether x + 2 is a factor of f(x)=−3x^5+2x^3−11x^2−38 How can Andrew use the factor theorem to determine whether x + 2 is a factor of f(x)? Drag a value, expression, or phrase into each box to correctly complete the statements.

Andrew evaluates f(−2) and determines its value to be −2. Andrew concludes that x + 2 is not a factor of f(x)=−3x^5+2x^3−11x^2−38

Jessica determines the remainder of 5x^52−4x^15−11x^2+12/x+1, using the remainder theorem. How does she proceed to the correct answer? Drag a value into each box to correctly complete the statements. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

Jessica evaluates the numerator of the rational expression when x=−1. She concludes that the remainder of the division is 10.

What is the upper bound of the function? f(x)=3x^4−7x^3+5x−3 Enter your answer in the box.

Upper bound = 3

What is the equation of the slant asymptote of the rational function? f(x)=6x^3−15x^2+x−4/3x^2−1

Y=2x-5

What is the solution to the rational inequality? 3x/x−3 ≤ 2/x−3

[2/3,3)

How does the multiplicity of a zero determine the behavior of the graph at that zero? Select answers form the drop-down menus to correctly complete the statements. A seventh degree polynomial function has zeros of −6, 0 (multiplicity of 3), 1 (multiplicity of 2), and 4. The graph of the function ________ the x-axis at −6. The graph of the function _________ the x-axis at 0. The graph of the function _________ the x-axis at 1. The graph of the function _________ the x-axis at 4.

crosses straight through crosses through while hugging is tangent to crosses straight through

What are the coordinates of the hole in the graph of the function? f(x)=3x−15/3x^2−11x−20 Enter your answer by filling in the boxes. Enter your answer as simplified fractions, as necessary.

hole= (5,3/19)

What is the graph of the function? f(x)=−1/x+2+3

https://static.k12.com/nextgen_media/assets/8358312-NP057_759_ChoiceB.png

Graph the solution to the inequality. −4√x−3< −8 Select the correct symbol and plot the solution to the inequality on the number line.

open circle pointing to the right from 7 x>7

f(x)=−3x4−3x3−8x+2 f(x)=3x3−8x2−x+1

x-> -∞= f(x)-> -∞ x-> ∞= f(x)-> -∞ x-> -∞= f(x)-> -∞ x-> ∞= f(x)-> ∞

Solve the equation. √x+12+2=√3x−8 Drag the choice or choices into the box to correctly state the solution to the equation.

x=24