Will you please correct any errors and add anything I missed.

 

 

Written Assignment 1
Answer all assigned exercises, and show all work. Each exercise is worth 5 points. 1. Find a second point on the line with slope m and point P, graph the line, and find an
equation of the line.
P2= (5,-.75) 1
m , P ( 2,1)
4
y1 4 x 2 1 If x =5=-.25(5+2) +1=-.25(7) +1=-.75 2. Find an equation of a line through the given point and (a) parallel to and
(b) perpendicular to the given line.
y 3( x 2) 1
a)
b) at (0, 3) y 3 x 0 3 y1 3 y 3x 3 x 0 3 y 1 x3
3 3. Find the domain of the function.
f ( x) 3 x 1
Due to the fact that it is a cubic root, the domain of the function are all real numbers or (∞,∞) WA 1, p. 1 4. Find the indicated function values.
3
f ( x) ;
x f (1), f (10), f (100), f (1/ 3) 3
3
1
3 (10) .3
10
3 (100) .03
100
3
( 1 ) 3 3 9
3
1
3 (1) 5. Find all intercepts of the given graph.
y x2 4x 4
y-intercept-set all x’s=0 y 0 4 0 4
2 y4 x-intercept-Factor
2
y x 2
y x 2 x 2 x20
x 2 Intercepts are (0,4)/(-2,0)
6. Factor and/or use the quadratic formula to find all zeros of the given function.
f ( x) x 2 x 12
y-intercept-set all x’s=0
2
y 0 0 12
y 12 x-intercept - Factor ( x) x 4 x 3
x1 4
x2 3 Intercepts are (0,-12)/(-4,0)/(3,0) WA 1, p. 2 7. Sketch a graph of the function showing all extrema, intercepts, and asymptotes.
(a) f ( x) 3 x 2 y-intercept
2
y 3 0 x-intercept(s) x 3 x y 3 x1 3 3x x2 3
(0,3)
Max[3-x2] is 3 @ x=0
(b) (-√3,0)/(√3,0) f ( x) x 2 20 x 11 y-intercept
2
y 0 20 0 11
y 11 0, 11 x-intercept(s)
f ( x ) x 2 20 x 11
x (20) (20)2 4(1)(11)
2(1) 20 356
2
x1 10 89, x2 10 89
x (10 89, 0), (10 89,0)
Max[-x2+20x-11] is 89 @ x=10
8. Sketch a graph of the function showing all extrema, intercepts, and asymptotes.
(a) f ( x) 10 x3 y-intercept x-intercept WA 1, p. 3 y 10 (0)3
y 10 10 x 3 0 x 3 10 (0,10) ( 3 10, 0) x 3 10 When graphed you can see that there is only one real zero. (b) f ( x) x 3 30 x 1
y-intercept
y (0)3 30(0) 1
y 1 x-intercept x3 30 x 1 0 (0, 1) x( x 30)( x 30) 1 0 x( x 2 30) 1 0
x1 0, x2 30, x3 30
( 30, 0), (0, 0), ( 30, 0) Max[-x3+30x-1]=20√10-1 @ x=√10
Min[-x3+30x-1]=-1-20√10@ x=-√10
9. Find all vertical asymptotes.
f ( x) x4
x2 9 x 2 9 0 x 3 x 3 The vertical asymptotes are at 3 and -3. x 3, 3 WA 1, p. 4 10. Determine whether the function has an inverse (is one-to-one). If so, find the inverse
and graph both the function and its inverse.
f ( x) x 2 1
When graphed this function does not pass the horizontal line test as stated on pg. 27 of our
textbooks. Also, inputting 1 and -1 for value ‘x’ gives the same output. 1 1 2 1 1 2 1 11. Convert the given radians measure to degrees.
(a) (b) 3
5 7 (c) 2 (d) 3 3 180 3 180 108o
5 5 180 180 25.71o
7 7 2 180 360 114.59o
1 3 180 540 171.89o
1 12. Convert the given degrees measure to radians.
(a) 40o 40 40 2
1 180 180
9 WA 1, p. 5 (b) 80o 80 80 4
1 180 180
9 (c) 450o 450 450 5
1 180 180
2 (d) 390o 390 390 13
1 180 180
6 13. Evaluate the inverse function by sketching a unit circle, locating the correct angle, and
evaluating the ordered pair on the circle.
tan 1 0 0o,360o
(1,0) 14. Evaluate the inverse function by sketching a unit circle, locating the correct angle, and
evaluating the ordered pair on the circle.
1 csc 2
30o,
6 3 1
, 2
2 15. A person who is 6 feet tall stands 4 feet from the base of a light pole and casts a 2-footlong shadow. How tall is the light pole?
WA 1, p. 6 tan opp 6 3
adj 2 tan opp
h tan 4 2 adj 4 2 h h 3 6 18 FT 6 feet
4 feet ᶿ
2 feet 16. Convert the exponential expression into fractional or root form.
42 1
1 2
4 16 17. Convert the exponential expression into fractional or root form.
6 2/5 5 62 5 36 18. Convert into exponential form.
4
x2 4x-2 19. Rewrite the expression as a single logarithm. WA 1, p. 7 2 ln 4 ln 3 ln42 –ln3ln16-ln3ln(16/3) 20. Rewrite the expression as a single logarithm.
ln 9 2 ln 3 ln9-ln32ln9-ln9ln(9/9)ln(1)0 WA 1, p. 8

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