Question

The table shows values for functions f(x) and g(x).

x f(x)=4x+20 g(x)=2x+6
−6 −4 1
−5 0 2
−4 4 4
−3 8 8
−2 12 16
−1 16 32
0 20 64

Answer 1

It seems you've provided a table that lists values for two functions, \( f(x) = 4x + 20 \) and \( g(x) = 2x + 6 \), evaluated at various values of \( x \). To analyze or compute any further information based on the values, let's first summarize the computed values of \( f(x) \) and \( g(x) \):

| x | f(x) = 4x + 20 | g(x) = 2x + 6 |
|-----|------------------|------------------|
| -6 | -4 | 1 |
| -5 | 0 | 2 |
| -4 | 4 | 4 |
| -3 | 8 | 8 |
| -2 | 12 | 16 |
| -1 | 16 | 32 |
| 0 | 20 | 64 |

### Summary of Values:
- For \( x = -6 \):
- \( f(-6) = 4(-6) + 20 = -24 + 20 = -4 \)
- \( g(-6) = 2(-6) + 6 = -12 + 6 = 1 \)

- For \( x = -5 \):
- \( f(-5) = 4(-5) + 20 = -20 + 20 = 0 \)
- \( g(-5) = 2(-5) + 6 = -10 + 6 = 2 \)

- For \( x = -4 \):
- \( f(-4) = 4(-4) + 20 = -16 + 20 = 4 \)
- \( g(-4) = 2(-4) + 6 = -8 + 6 = 4 \)

- For \( x = -3 \):
- \( f(-3) = 4(-3) + 20 = -12 + 20 = 8 \)
- \( g(-3) = 2(-3) + 6 = -6 + 6 = 0 \)

- For \( x = -2 \):
- \( f(-2) = 4(-2) + 20 = -8 + 20 = 12 \)
- \( g(-2) = 2(-2) + 6 = -4 + 6 = 2 \)

- For \( x = -1 \):
- \( f(-1) = 4(-1) + 20 = -4 + 20 = 16 \)
- \( g(-1) = 2(-1) + 6 = -2 + 6 = 4 \)

- For \( x = 0 \):
- \( f(0) = 4(0) + 20 = 0 + 20 = 20 \)
- \( g(0) = 2(0) + 6 = 0 + 6 = 6 \)

### Observations:
1. The function \( f(x) \) is always greater than or equal to \( g(x) \) for the values of \( x \) given in the table, except at \( x = -4 \) where they are equal.
2. The function \( f(x) \) increases at a faster rate than \( g(x) \) because the slope of \( f(x) \) is greater than the slope of \( g(x) \) (4 and 2, respectively).

If you have specific questions or require further analysis based on this data, feel free to ask!