The problem is asking for the range of the function $f(x) = 50x + 45$, which represents the total weight of a barbell plus $x$ pairs of weight plates.

Breakdown of the situation:

• The weight of the barbell alone is 45 pounds.
• Each pair of plates weighs 50 pounds.
• The function $f(x) = 50x + 45$ gives the total weight, where $x$ is the number of pairs of plates added to the barbell.

Constraints:

The maximum number of pairs of plates is 4, meaning $x$ can take the values 0, 1, 2, 3, or 4.

Range Calculation:

Using the given equation, let's find the total weight for each value of $x$:

• For $x = 0$, $f(0) = 50(0) + 45 = 45$
• For $x = 1$, $f(1) = 50(1) + 45 = 95$
• For $x = 2$, $f(2) = 50(2) + 45 = 145$
• For $x = 3$, $f(3) = 50(3) + 45 = 195$
• For $x = 4$, $f(4) = 50(4) + 45 = 245$

Therefore, the range is:

$\{ 45, 95, 145, 195, 245 \}$

This matches option B.

Would you like any further details or explanations?

Follow-up Questions:

1. How would the range change if more pairs of plates were added?
2. Can you express the domain of this function?
3. What would be the weight if you added 5 pairs of plates?
4. How is the slope of the function related to the problem?
5. What is the significance of the 45 pounds in the equation?

Tip:

The "range" refers to the set of all possible output values (weights) that the function can take, given the domain.