0. Functions

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = 2e⁻ˣ - 3

In Exercises 19–32, find the (a) domain and (b) range.

_____

𝔂 = -1 + ∛ 2 - x

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = 3 cos x + 4 sin x (Hint: A trig identity is required.)

Functions

In Exercises 1–6, find the domain and range of each function.

G(t) = 2/(t² − 16)

Functions

In Exercises 7 and 8, which of the graphs are graphs of functions of x, and which are not? Give reasons for your answers.

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Functions

In Exercises 7 and 8, which of the graphs are graphs of functions of x, and which are not? Give reasons for your answers.

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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.

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.

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.

Functions and Graphs

Find the natural domain and graph the functions in Exercises 15–20.

f(x) = 1 − 2x − x²

Functions and Graphs

Find the natural domain and graph the functions in Exercises 15–20.

g(x) = √−x

Functions and Graphs

Find the domain of y = (x + 3) / (4 − √(x² − 9)).

Functions and Graphs

Graph the following equations and explain why they are not graphs of functions of x.

a. |y| = x

Functions and Graphs

Graph the following equations and explain why they are not graphs of functions of x.

a. |x| + |y| = 1

Functions

In Exercises 1–6, find the domain and range of each function.

f(x) = 1 + x²