Question 1

Which of the following ordered pairs represents the midpoint of the segment with endpoints $$(-7, -5)$$ and $$(2, 13)$$?

Accepted Answer

$$( -2.5, 4 )$$

Question 2

Given points $$P(3, -5)$$ and $$Q(2, 8)$$, what is the distance between them?

Accepted Answer

$$\sqrt{194}$$

Question 3

Which equation represents a circle with center $$(1, -2)$$ and radius $$3$$?

Accepted Answer

$$(x-1)^2$$ + $$(y+2)^2 = 9$

Question 4

If the equation of a circle is $$x^2$$ + $$y^2 = 4$, what is the radius and center?

Accepted Answer

Center: $$(0,0)$$, Radius: $$2$$

Question 5

Which of the following relations is NOT a function?

Accepted Answer

$$P = \{(4,-3), (0,6), (2,8), (-4,-3)\}$$

Question 6

What is the general form of the equation of a circle?

Accepted Answer

$$x^2$$ + $$y^2 + Dx + Ey + F = 0$

Question 7

Given the equation $$y = -x^2$ + 1$$, which of the following points lies on its graph?

Accepted Answer

$$(0, 1)$$

Question 8

If the distance between points $$A(0, 0)$$ and $$B(4, 3) is$$ $$d$$, what is $$d$$?

Accepted Answer

$$5$$

Question 9

Which of the following is the correct formula for the midpoint $$M of a $$segment with endpoints $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 10

A circle has the equation $$x^2 + 4x$$ + $$y^2 - 8y = 45$. What is its center and radius?

Accepted Answer

Center: $$(-2, 4)$$, Radius: $$7$$

Question 11

Which of the following equations is symmetric with respect to the y-axis?

Accepted Answer

$$y = x^2$

Question 12

If $$y = \sqrt{x} + 1$$, what is the domain of this function?

Accepted Answer

$$[0, \infty)$$

Question 13

Which of the following is the correct formula for the distance between points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 14

If the equation $$x^2$$ + $$y^2 = -4$ is graphed, what does the graph represent?

Accepted Answer

No graph; the equation has no real solutions

Question 15

Which of the following is a solution to the equation $$y = -2x + 5$$?

Accepted Answer

$$(1, 3)$$

Question 16

A student claims the relation $$R = \{(1,2), (2,3), (1,4)\} is a $$function. Is the student correct?

Accepted Answer

No, because $$1 is $$paired with two different values

Question 17

Which of the following best describes the range of the function $$y = -x^2$ + 1$$?

Accepted Answer

$$(-\infty, 1]$$

Question 18

If the center of a circle is $$(h, k)$$ and the radius is $$r$$, what is the equation of the circle?

Accepted Answer

$$(x-h)^2$$ + $$(y-k)^2$$ = $$r^2$$

Question 19

Which of the following points is NOT on the graph of $$y = \sqrt{x} + 1$$?

Accepted Answer

$$(-1, 0)$$

Question 20

Suppose the total revenue for full-service restaurants in 2011 was $$194.6$$ billion and in 2017 was $$263.0$$ billion. Using the midpoint formula, what is the estimated total revenue for 2014?

Accepted Answer

$$(2014, 228.8)$$

Rectangular Coordinates, Graphs, and Circles: Precalculus Study Notes

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