Homework 1, due Tuesday, 23 SeptemberLibrary of Functions1. f(x) =√x(a) Determine algebraically whether f(x) is even, odd, or neither. What kind ofsymmetry does f(x) have?(b) Determine the intercepts, if any of the graph of f(x).(c) Graph f(x).(d) What is the domain and range of the function?(e) Where is the function increasing or decreasing? Does the function have any localmaxima or minima?2. f(x) =3√x(a) Determine algebraically whether f(x) is even, odd, or neither. What kind ofsymmetry does f(x) have?(b) Determine the intercepts, if any of the graph of f(x).(c) Graph f(x).(d) What is the domain and range of the function?(e) Where is the function increasing or decreasing? Does the function have any localmaxima or minima?3. f(x) = |x|(a) Determine algebraically whether f(x) is even, odd, or neither. What kind ofsymmetry does f(x) have?(b) Determine the intercepts, if any of the graph of f(x).(c) Graph f(x).(d) What is the domain and range of the function?(e) Where is the function increasing or decreasing? Does the function have any localmaxima or minima?4. f(x) = 1/x(a) Determine algebraically whether f(x) is even, odd, or neither. What kind ofsymmetry does f(x) have?(b) Determine the intercepts, if any of the graph of f(x).(c) Graph f(x).(d) What is the domain and range of the function?(e) Where is the function increasing or decreasing? Does the function have any localmaxima or minima?5. f(x) = x2(a) Determine algebraically whether f(x) is even, odd, or neither. What kind ofsymmetry does f(x) have?(b) Determine the intercepts, if any of the graph of f(x).(c) Graph f(x).(d) What is the domain and range of the function?(e) Where is the function increasing or decreasing? Does the function have any localmaxima or minima?6. f(x) = x3(a) Determine algebraically whether f(x) is even, odd, or neither. What kind ofsymmetry does f(x) have?(b) Determine the intercepts, if any of the graph of f(x).(c) Graph f(x).(d) What is the domain and range of the function?(e) Where is the function increasing or decreasing? Does the function have any localmaxima or minima?Other problems:• Section 3.1 #40, 93• Section 3.2 #11, 14, 24, 41• Section 3.3 #21, 22, 23, 25, 60, 63• Section 3.4 #32, 36, 47• Section 3.5 #19, 21, 23, 25, 42,