Question

Which function below has the largest slope?

Answer 1

Answer:

Option B is correct.

Slope of g(x) has the largest slope

Step-by-step explanation:

Point-intercept form:

The equation of line is in the form of $y=mx+b$ ......[1]

where m is the slope and b is the y-intercept.

In a given table:

x                    f(x)

2                    4

4                    12

6                    20

Slope is given by:

$m = \frac{y_2-y_1}{x_2-x_1}$

Consider any two values from the table:

(2, 4) and (4, 12)

then;

$m= \frac{12-4}{4-2}=\frac{8}{2}=4$

Therefore, the slope of the function f(x) is, 4

In g(x):

Given a function: g(x) =10x-4

On comparing with [1] we get;

Slope of g(x) = 10

In h(x)

Lance gains 1 level each time he plays his favorite video game. He started at level 10.

Let x be the the time

then;

h(x) = x+ 10

On comparing with equation [1] we have;

Slope of h(x) = 1

Thus:

Slope of g(x) > slope of f(x) > slope of h(x)

i.e  10 > 4 > 1

Therefore, function g(x) has the largest slope.

Answer 2

The slope of f(x) can be computed as
  (f(4) -f(2))/(4 -2) = (12 -4)/(2) = 8/2 = 4

The slope of g(x) is the coefficient of x
  10

The slope of h(x) is
  (1 level)/(1 play) = 1


The function with the largest slope is g(x).