Question

Question 1 A) Using the table below, for what x-values is f(x) > g(x)? x f(x) g(x) -2 7 -10 -1 4 -3 0 3 -2 1 4 -1 2 7 6 3 12 25 4 19 62 (1 point) Responses {−10,−3,−2,−1,6}{−10,−3,−2,−1,6}start set negative 10 comma negative 3 comma negative 2 comma negative 1 comma 6 end set {−2,−1,0,1,2}{−2,−1,0,1,2}start set negative 2 comma negative 1 comma 0 comma 1 comma 2 end set {12,19}{12,19}start set 12 comma 19 end set {7,4,3}{7,4,3}start set 7 comma 4 comma 3 end set Question 2 A) Using the table Compare f(x) and g(x). At how many points do the functions intersect? x f(x) g(x) -2 -7 -1 -1 0 0 0 1 1 1 2 2 2 9 3 (1 point) Responses 2 2 1 1 3 3 They do not intersect They do not intersect Question 3 A)Which of the following Characteristics is the same for ALL linear, Quadratic, and Exponential Functions?(1 point) Responses y-Intercept y-Intercept Maximum Maximum x-Intercept x-Intercept Domain Domain Range

Answer 1

### Question 1 A
To determine for which x-values \( f(x) > g(x) \), we can assess the values given in the table:

| x | f(x) | g(x) |
|----|------|------|
| -2 | 7 | -10 |
| -1 | 4 | -3 |
| 0 | 3 | -2 |
| 1 | 4 | -1 |
| 2 | 7 | 6 |
| 3 | 12 | 25 |
| 4 | 19 | 62 |

Now, let's compare \( f(x) \) and \( g(x) \):

- For \( x = -2 \): \( 7 > -10 \) (True)
- For \( x = -1 \): \( 4 > -3 \) (True)
- For \( x = 0 \): \( 3 > -2 \) (True)
- For \( x = 1 \): \( 4 > -1 \) (True)
- For \( x = 2 \): \( 7 > 6 \) (True)
- For \( x = 3 \): \( 12 < 25 \) (False)
- For \( x = 4 \): \( 19 < 62 \) (False)

The x-values for which \( f(x) > g(x) \) are \( -2, -1, 0, 1, 2 \).

**Answer:** {−2,−1,0,1,2}

### Question 2 A
To find the intersection points of \( f(x) \) and \( g(x) \):

| x | f(x) | g(x) |
|----|------|------|
| -2 | -7 | -1 |
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 9 | 3 | 3 |

Let's compare:
- At \( x = -2 \): \( -7 < -1 \)
- At \( x = 0 \): \( 0 = 0 \) (Intersection)
- At \( x = 1 \): \( 1 = 1 \) (Intersection)
- At \( x = 2 \): \( 2 = 2 \) (Intersection)

The functions intersect at 3 points: \( x = 0, 1, 2 \).

**Answer:** 3

### Question 3 A
The characteristic that is consistent across all linear, quadratic, and exponential functions is the **y-Intercept**. Each of these function types will have a y-intercept at the point where \( x = 0 \).

**Answer:** y-Intercept