Graph and analyze each function. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
1.f (x) = 5x2
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an even degree and a positive value for a.
D = ( , ), R = [0, ); intercept: 0; continuousforallrealnumbers
decreasing: ( , 0); increasing: (0, )
x 3 2 1 0 1 2 3 f (x) 45 20 5 0 5 20 45
2.g(x) = 8x5
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an odd degree and a positive value for a.
D = ( , ), R = ( , ); intercept: 0; continuousforallrealnumbers
increasing: ( , )
x 3 2 1 0 1 2 3 f (x) 1944 256 8 0 8 256 1944
3.h(x) = x3
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an odd degree and a negative value for a.
D = ( , ), R = ( , ); intercept: 0; continuousforallrealnumbers
decreasing: ( , )
x 3 2 1 0 1 2 3 f (x) 27 8 1 0 1 8 27
4.f (x) = 4x4
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an even degree and a negative value for a.
D = ( , ), R = ( , 0]; intercept: 0; continuousforallrealnumbers
increasing: ( , 0); decreasing: (0, )
x 3 2 1 0 1 2 3 f (x) 324 64 4 0 4 64 324
5.g(x) = x9
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an odd degree and a positive value for a.
D = ( , ), R = ( , ); intercept: 0; continuousforallrealnumbers
increasing: ( , )
x 3 2 1 0 1 2 3 f (x) 6561 170.7 0.3 0 0.3 170.7 6561
6.f (x) = x8
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an even degree and a positive value for a.
D = ( , ), R = [0, ); intercept: 0; continuousforallrealnumbers
decreasing: ( , 0); increasing: (0, )
x 3 2 1 0 1 2 3 f (x) 4100.6 160 0.625 0 0.625 160 4100.6
7.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an odd degree and a negative value for a.
D = ( , ), R = ( , ); intercept: 0; continuousforallrealnumbers
decreasing: ( , )
x 3 2 1 0 1 2 3 f (x) 1093.5 64 0.5 0 0.5 64 1093.5
8.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
The function is a monomial with an even degree and a negative value for a.
D = ( , ), R = ( , 0]; intercept: 0; continuousforallrealnumbers
increasing: ( , 0); decreasing: (0, )
x 3 2 1 0 1 2 3 f (x) 182.3 16 0.25 0 0.25 16 182.3
9.f (x) = 2x 4
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = (0, ); no intercepts; infinitediscontinuityatx = 0;
increasing: ( , 0); decreasing: (0, )
x 3 2 1 0 1 2 3 f (x) 0.025 0.125 2 2 0.125 0.025
10.h(x) = 3x 7
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = ( , 0) (0, ); no intercepts; infinite
discontinuity at x = 0; increasing: ( , 0) and (0, )
x 3 2 1 0 1 2 3 f (x) 0.001 0.023 3 3 0.023 0.001
11.f (x) = 8x 5
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = ( , 0) (0, ); no intercepts; infinite
discontinuity at x = 0; increasing: ( , 0) and (0, )
x 3 2 1 0 1 2 3 f (x) 0.03 0.25 8 8 0.25 0.03
12.g(x) = 7x 2
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = (0, ); no intercepts; infinitediscontinuityatx = 0;
increasing: ( , 0); decreasing: (0, )
x 3 2 1 0 1 2 3 f (x) 0.78 1.75 7 7 1.75 0.78
13.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = (, 0) (0, ); no intercepts; infinitediscontinuity
at x = 0; increasing: ( , 0) and (0, )
x 1.5 1 0.5 0 0.5 1 1.5 f (x) 0.01 0.4 204.8 204.8 0.4 0.01
14.h(x) = x 6
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = (0, ); no intercepts; infinitediscontinuityatx = 0;
increasing: ( , 0); decreasing: (0, )
x 1.5 1 0.5 0 0.5 1 1.5 f (x) 0.01 0.17 10.67 10.67 0.17 0.01
15.h(x) = x 3
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = ( , 0) (0, ); no intercepts; infinite
discontinuity at x = 0; decreasing: ( , 0) and (0, )
x 1.5 1 0.5 0 0.5 1 1.5 f (x) 0.22 0.75 6 6 0.75 0.22
16.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = ( , 0); no intercepts; infinitediscontinuityatx = 0;
decreasing: ( , 0); increasing: (0, )
x 1.5 1 0.5 0 0.5 1 1.5 f (x) 0.03 0.7 179.2 179.2 0.7 0.03
17.GEOMETRY ThevolumeofasphereisgivenbyV(r) = r3, where r is the radius.
a. State the domain and range of the function. b. Graph the function.
SOLUTION:a. The radius of a sphere cannot have a negative length. The radius also cannot be 0 because then the object wouldfail to be a sphere. Thus, D = (0, ), R = (0, )
b. Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
x 0.5 1 1.5 2 2.5 3 3.5 f (x) 0.5 4.2 14.1 33.5 65.5 113.1 179.6
Graph and analyze each function. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing.
18.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the denominator of the power is even, the domain must be restricted to nonnegative values.
D = [0, ), R = [0, ); intercept: 0; ; continuous on [0, ); increasing: (0, )
x 0 1 2 3 4 5 6 f (x) 0 8 9.5 10.5 11.3 12 12.5
19.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
D = ( , ), R = ( , ); intercept: 0; continuousforallrealnumbers
decreasing: ( , )
x 6 4 2 0 2 4 6 f (x) 8.6 7.9 6.9 0 6.9 7.9 8.6
20.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = ( , 0) (0, ); no intercepts; infinite
discontinuity at x = 0; increasing: ( , 0) and (0, )
x 1.5 1 0.5 0 0.5 1 1.5 f (x) 0.17 0.2 0.25 0.25 0.2 0.17
21.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the denominator of the power is even and the power is negative, the domain must be restricted to positive values.
D = (0, ), R = (0, ); no intercepts; ; continuous on (0, ); decreasing: (0, )
x 1 2 3 4 5 6 7 f (x) 10.0 8.9 8.3 7.9 7.6 7.4 7.2
22.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the denominator of the power is even, the domain must be restricted to nonnegative values.
D = [0, ), R = [0, ); intercept: 0; ; continuous on [0, ); decreasing: (0, )
x 0 1 2 3 4 5 6 f (x) 0 3 4.6 6 7.1 8.2 9.2
23.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
D = ( , ), R = ( , ); intercept: 0; continuousforallrealnumbers
increasing: ( , )
x 3 2 1 0 1 2 3 f (x) 1.45 1.13 0.75 0 0.75 1.13 1.45
24.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the denominator of the power is even and the power is negative, the domain must be restricted to positive values.
D = (0, ), R = ( , 0); no intercept; ; continuous on (0, ); increasing: (0, )
x 0.5 1 1.5 2 2.5 3 3.5 f (x) 0.84 0.5 0.37 0.3 0.25 0.22 0.2
25.
SOLUTION:Evaluate the function for several x-values in its domain.
Use these points to construct a graph.
Since the power is negative, the function will be undefined at x = 0.
D = ( , 0) (0, ), R = (0, ); no intercepts; infinitediscontinuityatx = 0;
increasing: ( , 0); decreasing: (0, )
x 3 2 1 0 1 2
