Chapter 4: Q. 39 (page 245)

Use the graph below of a polynomial function $y = f (x)$ to solve
$(a) f (x) = 0 (b) f (x) > 0 (c) f (x) \leq 0$
(d) determine f

Short Answer

Expert verified

(a)The function is 0 at $x = - 3, 2$ ,

(b) $f (x) > 0 a t x > - 3 a n d x > 2$ ,

(d) $f (x) = x^{3} - x^{2} - 8 x + 12$

Step by step solution

Step 1. Given Information

The given graph of the function is

Part(a) Step 1. Explanation

Locate the points on the graph where the function intersects the x-axis.

Thus, at $x = - 3 a n d x = 2$ the function is equal to 0.

Part(b) Step 1. Explanation

Determine the domain of the function for which the function is above the x-axis.

At $x > - 3 a n d x > 2$ the function is strictly greater than 0.

In the interval notation, $x : (- 3, \infty) \cup (2, \infty)$

Part(c) Step 1. Explanation

Determine the domain of the function for which the function is below or intersecting the x-axis.

At $x \leq - 3 a n d x = 2$ and in interval notation the solution is $x : (- \infty, - 3] \cup \{2\}$

Part(d) Step 1. Calculation

Use the zeroes from part (a) to produce a polynomial. Expand the linear factors.

$f (x) = (x + 3) (x - 2) (x - 2) = (x + 3) (x^{2} - 4 x + 4) = x^{3} - 4 x^{2} + 4 x + 3 x^{2} - 12 x + 12 = x^{3} - x^{2} - 8 x + 12$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use the graph below of a polynomial function $y = f (x)$ to solve
$(a) f (x) = 0 (b) f (x) > 0 (c) f (x) \leq 0$
(d) determine f

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Explanation

Part(b) Step 1. Explanation

Part(c) Step 1. Explanation

Part(d) Step 1. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the graph below of a polynomial function y=f(x)to solve(a)f(x)=0(b)f(x)>0(c)f(x)≤0(d) determine f

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Explanation

Part(b) Step 1. Explanation

Part(c) Step 1. Explanation

Part(d) Step 1. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the graph below of a polynomial function $y = f (x)$ to solve
$(a) f (x) = 0 (b) f (x) > 0 (c) f (x) \leq 0$
(d) determine f