Math 121, Practice Questions Hints And Answers (Page 3 of 5) in pdf

Math 121, Practice Questions Hints And Answers Page 3

7. Describe any symmetries (w.r.t. x-axis, y-axis or origin) the graphs of the following equa-

tions possess. Justify your answers.

(a) x = y + y + 1

Answer: Replacing y with

y yields: x = ( y) + ( y) + 1, that is x = y + y + 1 which is

the original equation. Thus there is symmetry over the x-axis. However, replacing x with

and replacing (x, y) with ( x, y) both change the equation, so the graph is not symmetric

with respect to the y-axis or origin.

(b) x + y = 10

Answer: Replacing y with

y; or x with

x; or (x, y) with ( x, y) all leave the equation

unchanged. Thus the graph is symmetric with respect to the x-axis, y-axis and origin.

11,

if x < 3;

8. Consider the piecewise deﬁned function f (x) =

2 if 3

1 if x > 8.

(a) Find: f (3)

Ans:

(b) Find: f (5)

Ans:

(d) Find f (r + 3) if r > 5

Ans:

4r + 11

Answer: Because r > 5, then r + 3 > 8 and so the last line of the formula should be used.

That is, f (r + 3) = 4(r + 3)

1 = 4r + 11.

9. Find the equation of the line through the points (4, 2) and (2, 8). Write your answer in

slope-intercept form.

( 2)

Answer: The slope is m =

5. Thus, plugging in (4, 2) we see that

2 =

5(4) + b, and so b = 18. Therefore, the equation of the line is

y =

5x + 18

Math 121, Practice Questions Hints And Answers Page 3