Student Activity: a Generic Function
Student Activity
A Generic Function
Use the generic graph of f(x) with domain [–6, –3] and [–2, 6] to answer the questions below.
7
Y
6
5
4
3
2
1
X
-7
-6 -5
-4 -3
-2 -1 0
-1
1
2
3
4
5
6
7
-2
-3
-4
-5
-6
-7
1.
What is the range of f(x)?
2.
What is the domain?
3.
On what intervals is f(x) decreasing?
4.
On what intervals will the following statements be true?
a)
As x increases, y increases.
b)
As x increases, y is constant.
c)
As x increases, y increases at a constant rate.
5.
For what values of x is f(x) > x?
6.
What is the absolute maximum value for f(x)?
7.
Give the coordinates of the point where the global minimum value of f(x) occurs.
8.
What is the absolute maximum value over the interval −6 ≤ x ≤ −3 ?
9.
For what values of x, x > 0, is f(x) concave down?
35
Student Activity
10.
Let
a)
b)
c)
g ( x) = f (− x)
Find g(–4) and g(2).
Determine the value of x where the maximum value of g(x) occurs.
Describe the transformation of the graph.
11.
Let
a)
b)
c)
g ( x) = − f ( x)
Find g(–2.5) and g(4).
Determine the minimum value of g(x).
Describe the transformation of the graph.
12.
Let
a)
b)
c)
g ( x ) = f (2 x )
Find g(–2) and g(1).
Determine the slope of g(x) on the interval [0, 2].
Sketch a graph of g(x).
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
1234567
36
x
Student Activity
13.
Let
a)
b)
c)
g ( x ) = f ( x − 1)
Find g(0) and g(1).
Determine the intervals where g(x) is increasing.
Sketch a graph of g(x).
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
1234567
x
14.
Let
a)
b)
c)
g ( x ) = f ( x + 3)
Find g(–2) and g(3).
If x > 0, determine where g(x) is concave down.
Describe the transformation of the graph.
15.
Let
a)
b)
c)
g ( x) = f ( x) + 3
Find g(–2) and g(3).
A Generic Function
Use the generic graph of f(x) with domain [–6, –3] and [–2, 6] to answer the questions below.
7
Y
6
5
4
3
2
1
X
-7
-6 -5
-4 -3
-2 -1 0
-1
1
2
3
4
5
6
7
-2
-3
-4
-5
-6
-7
1.
What is the range of f(x)?
2.
What is the domain?
3.
On what intervals is f(x) decreasing?
4.
On what intervals will the following statements be true?
a)
As x increases, y increases.
b)
As x increases, y is constant.
c)
As x increases, y increases at a constant rate.
5.
For what values of x is f(x) > x?
6.
What is the absolute maximum value for f(x)?
7.
Give the coordinates of the point where the global minimum value of f(x) occurs.
8.
What is the absolute maximum value over the interval −6 ≤ x ≤ −3 ?
9.
For what values of x, x > 0, is f(x) concave down?
35
Student Activity
10.
Let
a)
b)
c)
g ( x) = f (− x)
Find g(–4) and g(2).
Determine the value of x where the maximum value of g(x) occurs.
Describe the transformation of the graph.
11.
Let
a)
b)
c)
g ( x) = − f ( x)
Find g(–2.5) and g(4).
Determine the minimum value of g(x).
Describe the transformation of the graph.
12.
Let
a)
b)
c)
g ( x ) = f (2 x )
Find g(–2) and g(1).
Determine the slope of g(x) on the interval [0, 2].
Sketch a graph of g(x).
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
1234567
36
x
Student Activity
13.
Let
a)
b)
c)
g ( x ) = f ( x − 1)
Find g(0) and g(1).
Determine the intervals where g(x) is increasing.
Sketch a graph of g(x).
7
6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
y
1234567
x
14.
Let
a)
b)
c)
g ( x ) = f ( x + 3)
Find g(–2) and g(3).
If x > 0, determine where g(x) is concave down.
Describe the transformation of the graph.
15.
Let
a)
b)
c)
g ( x) = f ( x) + 3
Find g(–2) and g(3).