Question

Two linear functions are described below. Function f(x) has the equation f(x)=3x−4. Function g(x) has the table of values shown below. x g(x) 0 4 3 5 6 6 9 7 Which statement is true regarding the functions f(x) and g(x)? 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 slope of a linear function can be determined from its equation in the form
`y=mx+b` where
`m` is the slope.

a) For function
`f(x) = 3x -4`, the slope is 3.

b) To determine the slope for the function
`g(x)` from the table, we can choose two points from the table and calculate the slope using the formula
`(y2-y1)/(x2-x1)`

For the points (0, 4) and (3, 5):

Slope of
`g(x) = (5-4)/(3-0) = (1)/(3)`

The slope for the function
`g(x)` is
`(1)/(3)`

Now, comparing the slopes of the two functions:

Slope of
`f(x) = 3`

Slope of
`g(x) = (1)/(3)`

The slopes are not the same, and they are not opposites either. So, none of the options A or B is correct.

Now, let's check the y-intercepts:

c) The y-intercept for function
`f(x)` is -4

d) The y-intercept for the function
`g(x)` is 4 (when
`x`
`=0`)

The y-intercepts are not the same, and they are not opposites either. So, none of the options C or D is correct.

In conclusion, none of the given options is true regarding the functions
`f(x)` and
`g(x)`