Q: A medical researcher models the temperature $$T (in$$ °C) of a patient over time $$t (in $$hours) as $$T(t) = 37 + 2\sin(\frac{\pi}{12}t). $$What is the range of $$T$$?

$$[35, 39]$$ \text{ (since } \sin(\theta) \text{ ranges from } -1 \text{ to } 1)$

Question 1

Which of the following equations represents a graph that is NOT a function, according to the vertical-line test?

Accepted Answer

$$x = y^2$ - 3$$

Question 2

A set of points in the $$xy-$$plane is the graph of a function if and only if:

Accepted Answer

Every vertical line intersects the graph in at most one point.

Question 3

Given the function $$f(x) = \frac{x + 3}{x + 4}$$, what is the domain of $$f$$?

Accepted Answer

$$x 
eq -4$$

Question 4

Suppose $$f(x) = \frac{x + 3}{x + 4}. Is $$the point $$\left(1, \frac{3}{4}\right) on $$the graph of $$f$$?

Accepted Answer

Yes, because $$f(1) = \frac{3}{4}$$

Question 5

If $$f(x) = \frac{x + 3}{x + 4}$$ and $$x = 2$$, what is $$f(x)$$ and what point is on the graph?

Accepted Answer

$$f(2) = \frac{5}{6}$$, \ (2, \frac{5}{6})$

Question 6

If $$f(x) = \frac{x + 3}{x + 4}$$ and $$f(x) = 4$$, what is $$x$$?

Accepted Answer

$$x = \frac{13}{3}$$

Question 7

What are the $$x-$$intercepts of the graph of $$f(x) = \frac{x + 3}{x + 4}$$?

Accepted Answer

$$x = -3$$

Question 8

Which of the following best describes the range of $$f(x) = \frac{x + 3}{x + 4}$$?

Accepted Answer

$$y 
eq 1$$

Question 9

A real-world scenario: The height $$h (in $$meters) of a projectile at time $$t (in $$seconds) is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the domain of this function in the context of the problem?

Accepted Answer

$$0 \leq t \leq T$$ \ where $$T is $$when $$h(T) = 0$$

Question 10

Which of the following statements is TRUE about the graph of $$x^2$$ - $$y^2 = 1$?

Accepted Answer

It does not pass the vertical-line test and is not a function.

Question 11

If a graph fails the vertical-line test, what does this mean in a real-world context?

Accepted Answer

There is more than one output for a given input.

Question 12

Suppose $$f is a $$function whose graph passes through the points $$(0, 2)$$, $$(1, 3)$$, and $$(2, 5). $$What is $$f(1)$$?

Accepted Answer

$$3$$

Question 13

For the function $$f(x)$$, the line $$y = -1$$ intersects the graph three times. What does this tell you about the equation $$f(x) = -1$$?

Accepted Answer

It has three solutions.

Question 14

If $$f(x) \u003e 0$$ for $$x in $$the interval $$(1, 4)$$, what does this mean about the graph of $$f$$?

Accepted Answer

The graph is above the $$x-$$axis for $$1 \u003c x \u003c 4.$$

Question 15

Which of the following is NOT a valid way to obtain information from the graph of a function?

Accepted Answer

Finding the range by looking for all $$x-$$values with corresponding $$y-$$values

Question 16

A medical researcher models the temperature $$T (in$$ °C) of a patient over time $$t (in $$hours) as $$T(t) = 37 + 2\sin(\frac{\pi}{12}t). $$What is the range of $$T$$?

Accepted Answer

$$[35, 39]$$ 	ext{ (since } \sin(	heta) 	ext{ ranges from } -1 	ext{ to } 1)$

Functions and Their Graphs: Identification and Analysis

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