Question

The functions fx) and g(x) are both linear. The equation of f(x) is f(x) = 3x + 6.

The function g(x) has a slope of 6 and a y-intercept of 3.
Which statement about f(x) and g(x) is correct?
The two functions represent parallel lines.
© The two functions represent the same line,
©
The two functions intersect, and the value of RO) is less than the value of g(0).
The two functions intersect, and the value of f(0) is greater than the value of g(0).

Answer 1

The two functions intersect, and the value of
`f(0)` is greater than the value of
`g(0)`.

Explanation:

Given:

The function
`f(x) =3x+6`

The function
`g(x)` has slope 6 and y-intercept 3.

A linear function is of the form:
`y=mx+b`, where, 'm' is the slope and 'b' is the y-intercept.

Therefore, the equation of the function
`g(x)` with 'm' equal to 6 and 'b' equal to 3 is given as:

Also, the slope of function
`g(x)` is 3 and y-intercept is 6.

Now, option 1 is incorrect as their slopes are different.

Two lines of different slopes can't represent same line. So, option 2 is also incorrect.

`g(x)=6x+3`

The value of
`f(0) =3*0+6=6`

The value of
`g(0)=6*0+3=3`

Therefore, as 6 > 3,
`f(0)>g(0)`

Hence, the last option is correct.