Question

Given the following two functions:

f(x)= -5x+1

g(x)=-3x+2

Which statement is true

a
g(x) slope is less than f(x) slope

b
g(x) slope is greater than f(x)

c
g(x) intercepts the y axis is one unit above f(x)

Answer 1

To determine which statement is true about the functions \( f(x) = -5x + 1 \) and \( g(x) = -3x + 2 \), we need to analyze their slopes and y-intercepts.

1. **Slopes:**
- The slope of \( f(x) \) is -5.
- The slope of \( g(x) \) is -3.

Since -3 is greater than -5, we can conclude:
- The slope of \( g(x) \) is greater than the slope of \( f(x) \).

2. **Y-Intercepts:**
- The y-intercept of \( f(x) \) is 1 (from the equation it can be seen that when \( x = 0 \), \( f(0) = 1 \)).
- The y-intercept of \( g(x) \) is 2 (similarly, \( g(0) = 2 \)).

Therefore, \( g(x) \) intercepts the y-axis one unit above \( f(x) \).

Now summarizing the evaluation:

- **Statement a:** "g(x) slope is less than f(x) slope." **(False)**
- **Statement b:** "g(x) slope is greater than f(x)." **(True)**
- **Statement c:** "g(x) intercepts the y axis is one unit above f(x)." **(True)**

Thus, the true statements are:

- **b** and **c** are both correct.

However, if only one statement is to be selected, **b** is true regarding the slopes.