Domain and Range

Question

The function  gives the temperature, in degrees Fahrenheit, of a pot of water on a stove  minutes after the stove is turned on. After 30 minutes, the pot is taken off the stove.

The graph of the function is shown.

1. Is 250 in the range of function ? Explain how you know.
2. Describe the range of the function.
3. Does  have a solution? Explain how you know.

Answer 1

1. 250 is not in the range of the function W because the function never reaches 250 on the Y-axis of the graph. The range is simply the set of possible outcomes on the Y-axis.
2. The range of this graph would be (75, 212.5) because the lowest Y-value is 75 and the highest is 212.5
3. No, it doesn't have a solution because at no point does the graph reach 0 on the Y-axis which is what the question is asking. In words, the function says what is the value of t when W is 0.