MATH 107

02 Jul MATH 107

Use a ruler or a straight edge and draw a line segment between any two points in two different quadrants (no points on an axis can be used) in Figure 1 below.

a. Find the distance between those points you chose, label that distance on the line segment,

b. Find, plot, and label the midpoint of your line segment.

Figure 1 – Cartesian coordinates

Section 1.2

2. In your own words, briefly describe the difference between a relation and a function. (You can delete the lines and type if you need to)

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3. Which of the following is true about the x-intercept of a graph? (select more than one)

a. The x-intercept is a point that lies in Quadrant 1.

b. The x-intercept only lies on the x-axis.

c. X-intercept coordinates are of the form (0,a).

d. No one can show you what an x-intercept is, you have to see it for yourself.

4. To confirm symmetry about the y-axis for an equation such as y = x2 + 3x +2, you would do which of the following?

a. Substitute -y for y, then solve for y to get the original equation.

b. Add an x to both sides and see if the equation changes.

c. Substitute -x for x, then examine whether the equation is the same or not.

d. None of the above.

5. You have a function if the vertical line test affirms which of the following?

a. The graph touches the vertical line more than once for a single x value.

b. The graph only touches the vertical line once as it is swept from left to right.

c. The graph turns into a straight line.

d. None of the above.

Section 1.3

6. Select the relation that represents y as a function of x. Find the domain and range of those relations which are functions.

a. R = {(1,a), (1, b), (2,b), (3,c), (3, a), (4,a)}

b. R = {(1, 2), (1, 6), (2, 0.5), (5, 35), (9, 15), (9, 12)}

c. R = {(1,a), (2, b), (3,b), (4,c), (3, a), (4,a)}

d. R = {(1,a), (3, b), (5,b), (7,c), (9, a), (11,a)}

Domain: {____________________}

Range: {______________________}

Section 1.4

7. Given the function f(x) = 2/x:

a. State the domain in interval notation: ________________________

b. Find f(2): __________________

8. The area A enclosed by a circle, in square meters, is a function of its radius r, when measured in meters. This relation is expressed by the formula A(r) = _r2 for r > 0. Find A(2) and solve A(r) = 16_. Interpret your answers to each. Why is r restricted to r > 0?

9. For the following functions and , find .

a.

b.

c.

d. None of the above

Section 1.5

10. For the function , yields which of the following?

a.

b.

c.

d. None of the above

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