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Problem 18
Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1.
(ƒ/g)(5)
- Graph each function. See Examples 1 and 2. ƒ(x)=2/3|x|
Problem 19
Problem 19
For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).See Example 2. ƒ(x)={2+x if x<-4, -x if -4≤x≤2, 3x if x>2
- Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)
Problem 19
Problem 19
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
Problem 19a
For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2.
ƒ(x)=3x+4, g(x)=2x-5
Problem 19b
For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.
ƒ(x)=3x+4, g(x)=2x-6
Problem 19c
For the pair of functions defined, find (ƒg)(x).Give the domain of each. See Example 2.
ƒ(x)=3x+4, g(x)=2x-7
Problem 19d
For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2.
ƒ(x)=3x+4, g(x)=2x-8
Problem 20
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
Problem 21
Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32.
x-intercept (3,0), y-intercept (0,-2)
Problem 21
Graph each piecewise-defined function. See Example 2. ƒ(x)={x-1 if x≤3, 2 if x>3
Problem 21
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
Problem 21a
For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2.
ƒ(x)=2x^2-3x, g(x)=x^2-x+3
Problem 21b
For the pair of functions defined, find (ƒ-g)(x). Give the domain of each. See Example 2.
ƒ(x)=2x^2-3x, g(x)=x^2-x+3
Problem 21c
For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.
ƒ(x)=2x^2-3x, g(x)=x^2-x+3
Problem 21d
For the pair of functions defined, find (ƒ/g)(x). Give the domain of each. See Example 2.
ƒ(x)=2x^2-3x, g(x)=x^2-x+3
Problem 22
Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.
Problem 22
Graph each piecewise-defined function. See Example 2. ƒ(x)={6-x if x≤3, 3 if x>3
Problem 22
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
- Graph each function. See Examples 1 and 2. g(x)=(1/2)x^2
Problem 23
- Determine whether the three points are the vertices of a right triangle. See Example 3. (-6,-4),(0,-2),(-10,8)
Problem 23
Problem 23
Graph each piecewise-defined function. See Example 2. ƒ(x)={4-x if x<2, 1+2x if x≥2
Problem 23
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
Problem 23a
For the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
Problem 23b
For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
Problem 23c
For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
Problem 23d
For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
Problem 24
Determine whether the three points are the vertices of a right triangle. See Example 3.
Problem 24
Graph each piecewise-defined function. See Example 2. ƒ(x)={2x+1 if x≥0, x if x<0
