Question

learning goal
i can analyze and interpret the key features of a function using a graph or table. these key features include:

• intercepts
• intervals where the function is increasing, decreasing, positive or negative
• relative maximums and minimums
• end behavior

i can describe and sketch a graphic representation of a function given a verbal description of the relationship.
lesson 1.2 checkpoint

• once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.
• complete the lesson reflection above by circling your current understanding of the learning goal.

use the graph to answer problems 1 - 4.

1. which of the following intervals shows the graph increasing? select all that apply.

• a -2 < x < -1
• b -1 < x < 1
• c 1 < x < ∞

1. which of the following intervals shows the graph decreasing? select all that apply.

• a -2 < x < -1
• b -1 < x < 1
• c 1 < x < ∞

1. what are the coordinates of the local maximum?

(__,__)

1. what are the coordinates of the local minimum?

(__,__)

1. the graph shows a relationship between x and y. what are the zeros of the function?

x = __, and x = __

Explanation:

Step1: Identify increasing intervals

A function is increasing when the y - values increase as the x - values increase. Looking at the graph, the function is increasing on the intervals $-2 < x < - 1$ and $1 < x<\infty$.

Step2: Identify decreasing intervals

A function is decreasing when the y - values decrease as the x - values increase. The function is decreasing on the interval $-1 < x < 1$.

Step3: Find local maximum

The local maximum is the point where the function changes from increasing to decreasing. From the graph, the local maximum occurs at the point $(-1,4)$.

Step4: Find local minimum

The local minimum is the point where the function changes from decreasing to increasing. From the graph, the local minimum occurs at the point $(1, - 4)$.

Step5: Find zeros of the function

The zeros of the function are the x - values where $y = 0$. From the graph, the zeros are $x=-2$ and $x = 0$.

Answer:

1. A. $-2 < x < -1$, C. $1 < x <\infty$
2. B. $-1 < x < 1$
3. $(-1,4)$
4. $(1,-4)$
5. $x=-2$, $x = 0$