The function given is:

$f(x) = 40x + 10$

where:

• $f(x)$ represents the total weight of the barbell and plates in pounds.
• $x$ is the number of pairs of weight plates added to the barbell.
• Each pair of plates weighs 40 pounds, and the barbell itself weighs 10 pounds.

Domain:

Since $x$ represents the number of pairs of plates, the domain will typically be non-negative integers (i.e., $x \geq 0$).

Range:

To determine the range, let's look at how the function behaves as $x$ varies:

• When $x = 0$, the total weight is: $f(0) = 40(0) + 10 = 10 \text{ pounds}$
• As $x$ increases, the total weight increases linearly. Since there is no upper limit for $x$ mentioned, $f(x)$ can increase indefinitely.

Thus, the range of the function is: $f(x) \geq 10$ or in interval notation: $[10, \infty)$

This means the total weight will be at least 10 pounds and can increase without bound as more pairs of plates are added.

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Do you have any questions or would you like more details on how the range was determined?

Here are 5 related questions to further explore this topic:

1. What would the total weight be if 3 pairs of plates are added to the barbell?
2. How does the slope of 40 in the function $f(x) = 40x + 10$ affect the total weight as $x$ increases?
3. What is the meaning of the y-intercept (10) in the context of this problem?
4. How would the range change if each pair of plates weighed 30 lb instead of 40 lb?
5. What would the function look like if the barbell itself weighed 15 lb instead of 10 lb?

Tip: When analyzing functions like this, the y-intercept often gives the initial condition (in this case, the weight of the barbell), and the slope reflects how much the total changes with each added unit (here, the weight of each pair of plates).