Math 1050 - Exam 1 Review
1. Simplify the following so that only positive exponents remain:
1 5 0 2
ab c
a 3 b2 c2
2. Completely simplify the following:
x2
x2
9
5x
5x2+6 10x
3. For the points ( 7; 4) and (2; 8),
(a) Find the distance between the points using the distance formula.
(b) Find the midpoint of the line segment joining the two points using the midpoint
formula.
(c) Find the equation of the line passing through the two points. Write this equation
in slope-intercept form.
4. (a) Find the slope of the line through the points ( 5; 1) and (1; 5).
(b) Write an equation of the line that passes through ( 5; 1) with slope m = 32 . Write
your answer in slope-intercept form.
(c) Graph this line in the xy-plane. Label and scale your axes.
p
5. Solve for x: 3x 5 = x 1.
6. Find the equation of the circle with center at (2; 5) and radius, 4.
q
7. Consider the function f (x) = 9 259 x2 .
(a) What are the x- and y-intercepts? Make sure your answers are clearly labeled
ordered pairs, not just numbers.
(b) What kind of symmetry does the function have? Use algebraic tests to show this.
(c) What is the domain of the function?
(d) What is the range of the function?
7.
8. Find the domain of g(y) = y22y +64
9. Given f (x) = x2 + 2x + 1, nd f (x + hh) f (x) for h 6= 0.
10. Find the average rate of change of f (x) = x2 2x + 3 from x1 = 0 to x2 = 4.
p
11. Determine algebraically whether the function f (x) = x x2 + 29 is even, odd, or neither.
12. Sketch the graphs of the following parent functions:
(a) f (x) = jxj
1
(b) f (x) = x1
p
(c) f (x) = x
13. (a) Compared to the graph of f (x) = x2 , describe the transformation
g(x) = (x 3)2 + 5:
Horizontal shift
units to the
(right or left)
Vertical shift
units
(up or down)
Reection in the x-axis: YES or NO (circle one)
Reection in the y-axis: YES or NO (circle one)
(b) Use these answers to graph the transformation g(x) dened above. Be sure to
label and scale your axes.
14. Consider the function g(x) = (x + 3)3 2
(a) Describe the vertical shifts, horizontal shifts, and reections of this graph compared to the graph of f (x) = x3
(b) Graph g(x). Be sure to label and scale your axes.
8
if x < 0
< 2;
15. If f (x) = : x + 4; if 0 x 1 nd the following values:
1 x; if 1 < x
(a) f (0) =
(b) f ( 5) =
(c) f ( 21 ) =
(d) f (50) =
16. If f (x) = 3 2x and g(x) = x2 + 5x 1, nd the following and simplify:
(a) (f g)(x) =
(b) (fg)(x) =
(c) (f g)(x) =
(d) (g f )(x) =
17. Given f (x) = 3x + 5 and g(x) = 2x2 7x + 9, nd the following:
(a) g (x). What is the domain?
f
(b) (f g)(x).
18. Consider the function f (x) = 32xx + 14 .
(a) Find f 1(x), the inverse function of f .
(b) Find the domain and range of f and f 1.
19. Find the inverse of f (x) = 13 x3 4.
2