Question

Which function below has the smallest slope? f(x) f(x) = 2x − 3 g(x) graph going through (0, negative 5) and (4, 3) h(x) x h(x) −1 3 1 7 3 11

Answer 1

We have three functions:

FIRST.

$f(x)=2x-3$

The slope of f(x) is 2

SECOND.

g(x) graph going through (0, -5) and (4, 3), so:

We can find the slope of g(x) as follows:

$m=\frac{3-(-5)}{4-0}=\frac{8}{4}=2$

The slope of g(x) is 2

THIRD.

h(x) passes through (-1, 3), (1, 7) and (3, 11)

We can find the slope of h(x) as follows:

$Using \ points \ (-1, 3) \ and \ (1, 7) \\ \\ m=\frac{7-3}{1-(-1)}=\frac{4}{2}=2$

The slope of h(x) is 2

So, it is obvious that the three functions have the same slope 2.