Question

two linear functions are described below
Function f(x) has the equation f (x)=3x-4
function g(x) able of values shown below.

0 4
3 5
6 6
9 7

Which statement is true regarding the functions and ?
A.
The slopes of the two functions are the same.

B.
The slopes of the two functions are opposites.

C.
The y-intercepts of the two functions are the same.

D.
The y-intercepts of the two functions are opposites.

Answer 1

The equation for function f(x) is f(x) = 3x - 4.

To find the slope of function f(x), we can observe that the coefficient of x is 3. Therefore, the slope of function f(x) is 3.

To find the slope of function g(x), we can observe the change in the y-values as x increases by 3 units. We see that for every increase of 3 units in x, the corresponding y-value increases by 1 unit. Therefore, the slope of function g(x) is 1/3.

Based on the calculated slopes, we can conclude that statement A ("The slopes of the two functions are the same") is false.

To find the y-intercept of function f(x), we can set x = 0 in the equation f(x) = 3x - 4. When x = 0, f(x) = -4. Therefore, the y-intercept of function f(x) is -4.

To find the y-intercept of function g(x), we can observe the value of y when x = 0. We see that when x = 0, y = 4. Therefore, the y-intercept of function g(x) is 4.

Based on the calculated y-intercepts, we can conclude that statement C ("The y-intercepts of the two functions are the same") is false.

Therefore, the correct statement regarding the functions f(x) and g(x) is:

D. The y-intercepts of the two functions are opposites.