Answer:
Function A is a linear function and Function B is a nonlinear function
Function A has a positive rate of change
Step-by-step explanation:
Verify each statement
Option 1) Function A is a linear function and Function B is a nonlinear function
The statement is True
Because
Function A
The function A represent a proportional relationship that can be expressed in the form [tex]y=kx[/tex]
Find the value of k
For x=1, y=5 ----> [tex]k=\frac{5}{1}=5[/tex]
For x=2, y=10 ----> [tex]k=\frac{10}{2}=5[/tex]
For x=3, y=15 ----> [tex]k=\frac{15}{3}=5[/tex]
so
[tex]y=5x[/tex]
The graph is a straight line
therefore
Function A represent a linear function
Function B
we have
[tex]y=4x^2+2[/tex]
This is a quadratic equation (vertical parabola open upwards)
The graph is a curved line
therefore
Function B represent a nonlinear function, because the graph is not a straight line
Option 2) Function B has two y-intercepts at (0, 2) and (0, –2)
The statement is False
Because
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y=4(0)^2+2=2[/tex]
Therefore
The function B has only one y-intercept at (0,2)
Option 3) Function A has a positive rate of change.
The statement is True
Because
The rate of change of the function A is equal to the slope
The slope of the function A is m=5
Is a increasing function
As x increases the value of y increases
As x decreases the value of y decreases
Option 4) Function B has a negative rate of change
The statement is False
Because
To find the average rate of change, we divide the change in the output value by the change in the input value
we have
[tex]y=4x^2+2[/tex]
Is a vertical parabola open upward
The vertex of the function B is the point (0,2)
For the domain ----> (-∞,0)
The function is decreasing ( the rate of change is negative)
For the domain ----> (0,∞)
The function is increasing ( the rate of change is positive)
