Question

Which function below has the largest slope?

f(x)
x f(x)
2 4
4 12
6 20

g(x)
g(x)=10x − 4

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

Answers:
f(x)
g(x)
h(x)
The functions all have the same slope

Answer 1

Option B is correct.

Slope of g(x) has the largest slope

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 = (y_2-y_1)/(x_2-x_1)`

Consider any two values from the table:

(2, 4) and (4, 12)

then;

`m= (12-4)/(4-2)=(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).