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Problem 1.3.50
Using the Half-Angle Formulas
Find the function values in Exercises 47–50.
sin² 3π/8
Problem 1.1.52
Even and Odd Functions
In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.
g(x) = x⁴ + 3x² − 1
Problem 1.2.39
Graph the functions in Exercises 37–56.
y = |x − 2|
Problem 1.3.38
What happens if you take B = 2π in the addition formulas? Do the results agree with something you already know?
Problem 1.8
In Exercises 5–8, determine whether the graph of the function is symmetric about the 𝔂-axis, the origin, or neither.
𝔂 = e⁻ˣ²
Problem 1.1.56
Even and Odd Functions
In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.
h(t) = |t³|
Problem 1.1.50
Even and Odd Functions
In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.
f(x) = x² + x
Problem 1.4.26
Finding a Viewing Window
In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.
y = 3 cos 60x
Problem 1.4.35
Use graphing software to graph the functions specified in Exercises 31–36.
Select a viewing window that reveals the key features of the function.
Graph the function f (x) = sin 2x + cos 3x.
Problem 1.1.1
Functions
In Exercises 1–6, find the domain and range of each function.
f(x) = 1 + x²
Problem 1.3.36
Using the Addition Formulas
Use the addition formulas to derive the identities in Exercises 31–36.
sin (A − B) = sin A cos B − cos A sin B
Problem 1.4.20
Finding a Viewing Window
In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.
f(x) = (x² − 1)/(x² + 1)
Problem 1.23
In Exercises 19–32, find the (a) domain and (b) range.
𝔂 = 2e⁻ˣ - 3
Problem 1.3.31
Using the Addition Formulas
Use the addition formulas to derive the identities in Exercises 31–36.
cos (x − π/2) = sin x
Problem 1.1.5
Functions
In Exercises 1–6, find the domain and range of each function.
f(t) = 4/(3 − t)
Problem 1.4.36
Use graphing software to graph the functions specified in Exercises 31–36.
Select a viewing window that reveals the key features of the function.
Graph the function f (x) = sin³ x.
Problem 1.2.78
Graph the function y = √|x|.
Problem 1.19
In Exercises 19–32, find the (a) domain and (b) range.
𝔂 = |x| - 2
Problem 1.2.2
Algebraic Combinations
In Exercises 1 and 2, find the domains of f, g, f + g, and f ⋅ g.
f(x) = √(x + 1), g(x) = √(x − 1)
Problem 1.2.76
Graphing
In Exercises 69–76, graph each function not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation.
y = (−2x)²/³
Problem 1.1.14
Finding Formulas for Functions
Consider the point (x,y) lying on the graph of y = √(x − 3). Let L be the distance between the points (x,y) and (4,0). Write L as a function of y.
Problem 1.20
In Exercises 19–32, find the (a) domain and (b) range.
____
𝔂 = -2 + √1 - x
Problem 1.1.10
Finding Formulas for Functions
Express the side length of a square as a function of the length d of the square’s diagonal. Then express the area as a function of the diagonal length.
Problem 1.1.72
[Technology Exercise]
a. Graph the functions f(x) = 3/(x − 1) and g(x) = 2/(x + 1) together to identify the values of x for which
3/(x − 1) < 2/(x + 1)
b. Confirm your findings in part (a) algebraically.
Problem 1.35
Piecewise-Defined Functions
In Exercises 35 and 36, find the (a) domain and (b) range.
𝔂 = { √ -x, -4 ≤ x ≤ 0
{ √ x, 0 < x ≤ 4
Problem 1.1.12
Finding Formulas for Functions
A point P in the first quadrant lies on the graph of the function f(x) = √x. Express the coordinates of P as functions of the slope of the line joining P to the origin.
Problem 1.4
A hot-air balloon rising straight up from a level field is tracked by a range finder located 500 ft from the point of liftoff. Express the balloon’s height as a function of the angle the line from the range finder to the balloon makes with the ground.
Problem 1.2.80
Can a function be both even and odd? Give reasons for your answer.
Problem 1.4.33
Use graphing software to graph the functions specified in Exercises 31–36.
Select a viewing window that reveals the key features of the function.
Graph four periods of the function f (x) = −tan 2x.
Problem 1.3.48
Using the Half-Angle Formulas
Find the function values in Exercises 47–50.
cos² 5π/12