Download Exam 1 Review Problem 1 Write the standard and general form of a

Exam 1 Review
Problem 1 Write the standard and general form of a circle with center (h, k) =
(2, −3) and radius r = 5.
Answer: (x − 2)2 + (y + 3)2 = 25.
Problem 2 Find the center, radius, and intercepts (if any) of the circle x2 + y 2 −
6x + 10y + 25 = 0.
Answer: center = (3,-5), radius = 3, no x-intercepts, y-intercept at -5
Problem 3 Determine whether the equation 2y 2 + 3x2 = 4 determines y as a function
of x. If not, explain why. If so, determine its domain.
q
Answer: Not a function since y = ± 2 − 32 x2 and if x = 0, then y = ±2 so given one
value of x there are two possible values of y.
Problem 4 Find the domain of the function f (x) = √
1
.
x + 10
Answer: (−10, ∞) or all numbers x with x > −10.
2x
. Find the domain, the x and y intercepts
+1
of its graph, and find all points x such that f (x) = 1.
Problem 5 For the function f (x) =
x2
Answer: Domain is all real numbers, x intercept is 0, y intercept is 0, the only value
of x such that f (x) = 1 is x = 1.
Problem 6 Sketch the graph of the function f (x) = (x − 2)3 + 8 and find the x and
y intercepts.
Answer: See your calculator for what your solution should look like.
x2 − 4
, x > 4 (Now it should be
Problem 7 Find the inverse of the function f (x) =
2x2
the positive square root).
√
Answer: f −1 (x) = ± −42y − 1
Problem 8 For the right triangle triangle with legs of length 5 and 6, compute the
values of the 6 trigonometric functions for the angle θ opposite the side of length 5.
√
√
√
√
cos(θ) = 5 61/61, sin(θ) = 6 61/61, tan(θ) = 5/6, sec(θ) = 61/5, csc(θ) = 61/6,
cot(θ) = 6/5
Problem 9 If csc(θ) =
tions.
√
5, determine the values of the other five trigonometric func-
1
Answer: cos(θ) =
√
5 61
,
61
sin(θ) =
√
6 61
,
61
tan(θ) = 5/6, sec(θ) =
√
61/5, cot(θ) = 6/5
Problem 10 Compute the exact value of the expression 2 cos2 (9.6◦ ) + 2 sin2 (9.6◦ ).
Answer: 2
Problem 11 Find the exact value of the expression 3 cos
Answer:
√
3 2
2
−
π
4
− tan
π
3
√
3
Problem 12 Find the exact value of the expression −2 sin(π/6) cos(π/4) + sin(π/3).
Answer:
√
1− 6
2
2