Question

The function f(x) is shown in this graph

Answer 1

Answer:

The correct statement is:

• The slope of f(x) is same as the slope of g(x)

Step-by-step explanation:

• We see that the graph of the function f(x) is a line that passes through (0,2) and (1,-1)

Hence, the equation of the function f(x) is calculated by a two-point formula as:

$y-2=\dfrac{-1-2}{1-0}\times (x-0)\\\\y-2=\dfrac{-3}{1}\times x\\\\y-2=-3x\\\\y=-3x+2$

( On comparing the equation of f(x) with slope intercept form.

i.e. y=mx+c

where m is the slope and c is the y-intercept)

We get slope of f(x)= -3

and y-intercept= 2

• The function g(x) is given by:

$g(x)=-3x-6$

Hence, slope of g(x) = -3

and y-intercept= -6

Hence, we get that the slope of f(x) and g(x) is same.

( i.e. -3)