Algebra Questions

4 Le f be defined as f x x 1 2x 1 Find f 3 in two different ways One Way Find f and then compute f 3 Another way Solve for x f y x 1 2x 1 X 3

5 Let f x 2 x 3 a Show that f is one to one f x x 3 f x x 3

The graph of f x is shown in red Draw the graph of g x f x Make sure to start at one of the endpoints not the middle point After finishing the graph click outside the grid to stop drawing 8 7 6 5 4 3 2 7 8 96 5 4 3 2 1 2 3 4 5 69 7 8 1 Clear All Draw Polygon 2 3 4 5 6 7 8

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f a The slope is Type an integer or a simplified fraction 10 8 230 200 160 20 80 40 240 80 120 160 200 240 280

Suppose f and g are inverse If f 3 5 find g 5

Solve the polynomial inequality and graph the solution set on a real number line Express the solution set in interval notation x 7x 10 0 Use the inequality in the form f x 0 to write the intervals determined by the boundary points as they appear from le to right on a number line Interval Sign Type your answers in inf positive negative ascending order

Solve the rational inequality and graph the solution set on a real number line Express the solution set in interval notation X 5 30 Move all terms to the left side of the inequality and then define the left side of the inequality as f x Then list the intervals determined by the real zeros of f and the real numbers for which f is undefined Complete the following table Interval Sign Type your answers ir negative se ascending order

Find the equation for a polynomial f x that satisfies the following Degree 5 Root of multiplicity 2 at x 3 Root of multiplicity 1 at x 2 Root of multiplicity 2 at x 3 y intercept of 0 324 f x help formulas

QUESTION 4 2 points A population of punishers is described by the DTDS 1 0 5 1800 where T is the density after t weeks FIND the general Solution of the DTDS if initially to 1000

Find the equation for a polynomial f x that satisfies the following I Degree 3 Zero at x 3 Zero at x 1 Zero at x 3 y intercept of 0 8 f x help formulas

nd the polynomial in the second numerator such that the following statement is true x 16 x 5x 4 3x 10x 8 1

Let the graph of f x be given below Find the formula of f x a polynomial function of least degree 18 Click on graph to enlarge f x help formulas

Find the zeros and give the multiplicity of each for f x x x 4 x 2 Note to be counted as correct you must get One zero is a Another zero is x The last zero is x all answers correct and has a multiplicity of and has a multiplicity of and has a multiplicity of help numbers help numbers help numbers

Factor the polynomial function f x 10 9r 3x 2 The zeros are f x

Question 3 Let f x 22x 189x 248r 21 According to the rational roots theorem which of the following does NOT represent a possible pair of rational roots of this polynomial 7 11 21 21 22 11 1 3 3 22 70 Question Help Message instructor 1 11 3 21 22 2 O 3 11

Which graph best represents the solution set of y 4x B D 6 5 4 3 TETE DE ASS PA

The graph of 2x 5y 10 Is shown on the grid 30 A 0 5 B 5 0 C 2 5 D 5 2 Y 10 31 enn M 15 9 Which ordered pair is in the solution set of 2x 5y2 10 a X

A linear function is shown in the graph below What is the rate of change of this function record your answer as a decimal 8 3 3 4 5

8 Jim and Joe are brothers Joe is 30 older than Jim If Joe is 39 how many years older is he than Jim 130 39

Example 3 If an astronaut visited Jupiter he would weigh about 140 more on Jupiter than on Earth due wity If the astronaut weighs 160 pounds on Earth how much would he

Find a polynomial of degree n that has the given zero s There are many correct answers x 7 n 2 f x

4 Nicole spends 15 minutes completing her math homework and looking over her notes each night However after her first quiz she isn t happy with her grade She decides to increase the amount of time she spends on math by 75 How many minutes does she now spend working on math each night

Homework 10 22 1 Car prices for a certain car are projected to increase 125 in 10 years If a car currently is sold for 6000 how much would it be sold for in ten years

3 Kayla calculates that she ll spend 75 more money if she orders takeout for all of her din ners for a week than if she cooks the meals herself If she would spend 60 to cook for herself how much would takeout cost

8 Jim and Joe are brothers Joe is 30 older than Jim If Joe is 39 how many years older is he than Jim

2 An adult ticket to a movie costs 40 more than a child s ticket to a movie If adult tickets cost 10 50 how much does a child s ticket cost

3 Ed earns a 15 pay raise If he now earns 1200 each week how much money did he earn before the increase rounded to the nearest cent if needed a 180 00 P 1020 00 c 1043 48 d 8000 00

4 Last year the budget for the Winter Dance was 500 This year it increased by 20 How much was the budget for the dance this year a 400 b 520 A 600 d 1000

2 Ms Hollis decides to let her students vote on whether the final project should be completed independently or in groups 50 more students wanted to complete the project in groups than wanted to complete the project independently If 60 students wanted to complete the project in groups how many people wanted to complete it independently a 10 b 20 C30 d 40

1 The winning team in a football game scored 20 more points than the losing team If the ing team scored 35 points how many did the winning team score a 7 42 c 45 d 55

5 Miguel spends 702 on bills 204 on utilities and 1200 on rent every month The total amount he spends on these necessities is 35 percent more than he spontyoors g How

2 John is training for a bike race Over his training program he increases his weekly mileage by 25 At the end of his training program he bikes 243 miles in a week How far was he biking at the beginning of the week

Score 2 10 Penalty none Question Answer the questions about the following polynomial Answer Attempt 1 out of 2 The expression represents a is 10 6 and the leading coefficient is Submit Answer polynomial with Watch Video terms The constant term is Show Examples 0 the leading term

What is the solution set of the equation 2 9 Note q 0 1 O 1 4 o 4 4 2 O 2 4 q 4 9 1

What is the solution set of the equation2 2 Note j0 2 O 1 1 o 2 O 1 2 o 1

QUESTION 1 2 points FIND The Domain of the function f x 2 T 9 7x

Heather wrote this solution to solve for x Which statement is true 1 is an extraneous solution because it creates a 0 in the denominator O 5 is an extraneous solution because it creates a 0 in the denominator O There are no extraneous solutions O Both 1 and 5 are extraneous solutions because they create a 0 in the denominator 6 x 9x 20 6 x 5 x 4 x 4 x 5 x 4 x 5 x 4 1 x 1 X 4 X 5 1 x 1 X 4 x 5 H H x 5 x 1 x 4 6 x 5 x 4x x 4 6 0 x 4x 5 0 x 5 x 1 x 5 or x 1 6 x 5 x 4 x 5 x 4 Factor Multiply by the LCD Simplify Simplify Combine like terms Zero Product Property Solve for x

What is the solution to the equation 7 5 2 Enter your answer in the box

Use the remainder theorem and synthetic division to find f k for the given value of k f x x 7x 11x 1 k 5 f 5

A company has created an equation f x 5 10 that represents their business profits f x in thousands if they sell x number of products in hundreds A picture of the graph of this function is below Determine if the statements below are true or false based on the interpretation of the key features of the function in context 5 business profits in thousands of dollars 50 5 10 10 number of products sold in hundreds 15 The business will start making profit after they sell 1000 products The business profits are increasing from 0 00 They spent 10 000 to start their company e point 9 5 represents that if the company sells 500 products they will have a profit of 9 000 As the company sells more products their profits increase An appropriate range for this function is 0 0 True False

Use synthetic division to decide whether the given number k is a zero of the given polynomial function If it is not give the value of f k f x x 4x 8x 15 k 3 Is 3 a zero of the function Select the correct choice below and if necessary fill in the answer box to complete your choice O A OB The given k is not a zero of the polynomial function f 3 Simplify your answer The given k is a zero of the polynomial function

For the following polynomial function use the remainder theorem to find f k f x 3x5 9x 19x 40 k 2 f 2 Simplify your answer

Express f x in the form f x x k q x r for the given value of k f x x 7x 13x 6 k 2 f x

Express f x in the form f x x k q x r for the given value of k f x 2x x x 8 k 1 f x

Use synthetic division to perform the following division x4 4x 4x 21x x 3 x4 4x 4x 21x x 3 Simplify your answer Use integers or fractions for any numbers in the expression

Write an equation any form for the quadratic graphed below 6 5 4 2 6 S 4 3 2 2 3

3 2 2C Understand the relationship between zeros and factors in polynomials NM PT AT Let g be a polynomial function of x where g x 1 If x 3 is a factor of g what is the remainder of g x x 3 f x Write an equation for g as the product of linear factors g x 2x 5x 28x 15 3 4 Let f be a polynomial function of x where f x x 8x 20x 16 We know that f 2 0 f 0 16 and f 2 96 Use that knowledge to re write f x in factored form The input of 2 produces an output of 0 What other input s produce an output of 0 How do

2 Use the expression to answer the question x y 8 x 3 Y Which of the following answer choices is the simplified from of the given expression 1 A x3y x yl g

Look at the graph of the function f x x 1 3 below and describe its charact 0 1 3 Domain 5 Range Positive Interval Interval of Negative Interval as x as x V V 10 10 0 average rate of change over the interval 2 5 The point 10 0 is the 15 1 00 f x f x V V V

Write an equation any form for the quadratic graphed below 6 5 3 6 5 4 3 2 4 2 3 S A k 16