The image displays a graph of a cubic function plotted on a coordinate plane. The graph is characterized by:- **Axes:** The horizontal axis is labeled as $x$ and the vertical axis is labeled as $y$.- **Scale:** Both axes have markings at intervals of 10 units ranging from $-10$ to $10$.- **Plot:** The curve represents the behavior of a cubic polynomial, showing typical features such as turning points and intercepts.### Key Features:1. **Turning Points:** - The curve has two turning points. - It first increases, reaches a maximum, then decreases to a minimum, and finally increases again.2. **Intercepts:** - The curve intercepts the $y$-axis close to the origin. - The $x$-axis intercepts are located between the turning points, indicating roots of the polynomial.This graph is useful for understanding the dynamic nature of cubic functions, showcasing their ability to change direction and intersect axes multiple times. **Consider the function shown in the following graph.***[Graph displays a curve that increases from left to right, reaches a peak, decreases to a trough, and then increases again.]***Note:** you can click on the graph to enlarge it.**Question:** Where is the function decreasing?**Answer:** [Input box]**Note:** use interval notation to enter your answer.

For the graph given, The critical points (where the slope of curve is 0) are: x = -1 and x = 4The function is decreasing on the interval, x∈-1,4

Answered: Consider the function shown in the…

Math

Calculus

Consider the function shown in the following graph. Note: you can click on the graph to enlarge it. Where is the function decreasing? Note: use interval notation to enter your answer.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

The image displays a graph of a cubic function plotted on a coordinate plane. The graph is characterized by:

- **Axes:** The horizontal axis is labeled as $x$ and the vertical axis is labeled as $y$.
- **Scale:** Both axes have markings at intervals of 10 units ranging from $-10$ to $10$.
- **Plot:** The curve represents the behavior of a cubic polynomial, showing typical features such as turning points and intercepts.

### Key Features:

1. **Turning Points:**
- The curve has two turning points.
- It first increases, reaches a maximum, then decreases to a minimum, and finally increases again.

2. **Intercepts:**
- The curve intercepts the $y$-axis close to the origin.
- The $x$-axis intercepts are located between the turning points, indicating roots of the polynomial.

This graph is useful for understanding the dynamic nature of cubic functions, showcasing their ability to change direction and intersect axes multiple times.

**Consider the function shown in the following graph.**

*[Graph displays a curve that increases from left to right, reaches a peak, decreases to a trough, and then increases again.]*

**Note:** you can click on the graph to enlarge it.

**Question:** Where is the function decreasing?

**Answer:** [Input box]

**Note:** use interval notation to enter your answer.

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