GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A nutritionist is monitoring a patient's weight during a diet program. The patient's weight, W (in pounds), after d days is modeled by the function W(d) = 200 - 0.5d. What does the y-intercept of this function represent in the context of the patient's weight?
- AThe number of days to reach target weight.
- BThe daily weight loss rate.
- CThe patient's starting weight.
- DThe patient's target weight.
Show answer & explanationAnswer & explanation
Correct answer: C. The patient's starting weight.
The y-intercept of a function is the value of the dependent variable (W) when the independent variable (d) is 0. In this context, when d = 0 (at the beginning of the diet), W(0) = 200 - 0.5(0) = 200. This 200 pounds represents the patient's starting weight.
Why the other options are wrong
- A. The number of days to reach a target weight would be found by setting W(d) equal to the target weight and solving for d.
- B. The daily weight loss rate is represented by the slope (-0.5), not the y-intercept.
- D. The target weight is not explicitly given by the y-intercept; it's a goal, not an initial condition.
Y-intercept in Context
The y-intercept of a function (the value of y when x=0) represents the initial amount, starting value, or fixed cost in a real-world scenario.
- Always occurs when the independent variable (x) is zero.
- Represents the 'beginning' state or fixed value.
- Found by setting x=0 and solving for y.
- Crucial for understanding initial conditions in models.
Memory trick: Y-Intercept: X is Zero, It's the Start!