Download Day 1

MATH 125 – CALCULUS I
FALL 2016
PREREQUISITE REVIEW
1. Express as an inequality involving absolute value.
(a) [−2, 2]
(b) (0, 4)
(c) (−2, 8)
2. Find the domain and range of the following functions.
(a) f : [r, s, t, u] → [A, B, C, D, E]
where f (r) = A, f (s) = B, f (t) = B, and f (u) = E
(b) g(t) = t4
(c) f (x) = −x
3. Determine whether the equation defines y as a function of x.
(a) x = y 3
(b) x2 + y = 9
4. Sketch f (x) = x2 − 4. Determine symmetry, and label where the graph is increasing
or decreasing.
5. Suppose f has domain [4,8] and range [2,6]. Find the domain and range of:
(a) y = f (x) + 3
(b) y = f (x + 3)
(c) y = f (3x)
(d) y = 3f (x)
6. Show that the sum of two even functions is even and the sum of two odd functions is
odd.
7. Find the equation of the line with the following description:
(a) slope 3, y-intercept 8
(b) horizontal, passes through (-2, 2)
(c) perpendicular to 3x + 5y = 9, passes through (2, 3).
8. Complete the square and find the maximum or minimum of the quadratic function
y = x2 + 2x + 5
9. Find the roots of the quadratic functions:
(a) f (x) = 4x2 − 3x − 1
(b) f (x) = x2 − 2x − 1
10. Calculate the composite functions g ◦ f and f ◦ g where g(x) = x + 1 and f (x) =
Find the domain of the composite functions.
11. Find all values of c such that f (x) =
x+1
x2 +2cx+4
p
(x).
has domain R.
12. Write the equation for the piecewise function that equals three when x is less than zero
and equals x2 + 3 when x is greater than or equal to zero. Sketch the graph of this
function.
13. Describe θ =
π
6
by an angle of negative radian measure.
14. Find the angles between 0 and 2π satisfying the given conditions.
(a) tan(θ) = 1
(b) csc θ = 2
(c) sec t = 2
15. Find sin(θ), cos(θ), and sec(θ) if cot(θ) = 4.
16. Find a domain on which f is invertible and find its inverse.
(a) f (x) = 3x − 2
(b) f (s) =
(c) f (x) =
1
s2
1
x+1
17. Use triangle and trigonometric identities to compute:
(a)
Without using a calculator, calculate
(a) log3 27
(b) log5
1
25