Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes?

f(x) Alex earns 1600 dollars in 400 hours.
x
g(x)
1
−8
5
12
9
32

Answer 1

f(x) = 1600/400 reduces to 4....the slope of f(x) is 4

g(x) :
(1,-8)(5,12)
slope = (12 - (-8) / (5 - 1) = (12 + 8)/4 = 20/4 = 5...slope of g(x) is 5

so g(x) has a greater slope then f(x)

Answer 2

As per the statement:

Below are two different functions, f(x) and g(x).

For f(x):

Alex earns 1600 dollars in 400 hours.

`\text{unit rate per hour} = (1600)/(400) = 4` dollars.

Slope of f(x) = 4

Now, find the slope of g(x):

Formula for slope is given by:

`\text{Slope} = (y_2-y_1)/(x_2-x_1)`

From the given tables:

Consider two values (x, g(x)) i.e,

(1, -8) and (5, 12)

Then;

`\text{Slope} = (12-(-8))/(5-1)`

⇒
`\text{Slope} = (20)/(4) =5`

⇒Slope of g(x) = 5

`\text{Slope of g(x)} > \text{Slope of f(x)}`

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