Isaiah is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x)=\frac{1}{25}\big(\left|7x\right|+5x\big)f(x)=251(∣7x∣+5x) will determine how many calories Isaiah will burn if he runs up xx steps. Use a negative value for xx if he runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.

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MrRoyal MrRoyal · Answer 1 · 2021-10-05T19:25:13+02:00

The intercept of a function are the values of the function when the graph crosses the x or y axes.

The function is given as:

[tex]\mathbf{f(x) = \frac 1{25}(|7x| + 5x)}[/tex]

Set x to 0, to calculate the y-intercept

[tex]\mathbf{f(0) = \frac 1{25}(|7 \times 0| + 5\times 0)}[/tex]

[tex]\mathbf{f(0) = \frac 1{25}(|0| + 0)}[/tex]

[tex]\mathbf{f(0) = \frac 1{25}(0)}[/tex]

[tex]\mathbf{f(0) = 0}[/tex]

Set f(x) to 0, to calculate the x-intercept

[tex]\mathbf{ \frac 1{25}(|7x| + 5x) = 0}[/tex]

Multiply through by 25

[tex]\mathbf{ |7x| + 5x = 0 \times 25}[/tex]

[tex]\mathbf{ |7x| + 5x = 0}[/tex]

Remove absolute bracket

[tex]\mathbf{ 7x + 5x = 0}[/tex]

[tex]\mathbf{ 12x = 0}[/tex]

Divide through by 12

[tex]\mathbf{ x = 0}[/tex]

Hence, the intercepts are 0

This interpretation is that:

Isaiah's starting position is on the ground (a step before the staircase)

Because he can move up and down the staircase, where the up and down movements represent negative and positive direction

The appropriate domain is: [tex](-\infty, \infty)[/tex]

Read more about domains and intercepts at:

https://brainly.com/question/24123211