Inverses Practice
Precalculus HS Mathematics Unit: 02 Lesson: 02
Inverses Practice For each function, on the same set of axes, sketch the graph of its inverse relation. Tell whether this inverse is also a function by writing YES or NO. 1) 2)
3)
4)
5) Restrict the domain of this quadratic function so that it is invertible. Then sketch the inverse function.
Domain restriction for y = f(x): ______________
©2012, TESCCC
05/17/12
Sketch y = f −1( x )
page 1 of 2
Precalculus HS Mathematics Unit: 02 Lesson: 02
Inverses Practice 6) Name an interval (domain) on which g (x ) would be invertible. Then sketch g −1( x ) on the same graph.
Domain restriction for g (x ) : ______________
s(t) 0 5 15 33 45 50 50 50
The given graph and table describe the function s(t), which gives the speed (s in mph) of an automobile as it accelerates over a period of 8 seconds (t).
60 50 Speed (mph)
t 0 1 2 3 5 6 7 8
40 30
7) Explain why s(t) is not invertible, but can be if the domain is restricted to [0, 6].
20 10 0
1
2
3 4 5 6 Time (seconds)
7
Let s −1(t ) represent the inverse function of s(t) (when its domain is restricted to [0, 6]). 8) Estimate the value of s(4). Explain what this means in the situation.
9) Estimate the value of s −1(25) and s −1(35) . Explain what these mean in the situation.
10) Sketch the graph of s −1(t ) on the grid provided. 11) Find the value of s −1(s(5)) . Explain what this means in the situation.
©2012, TESCCC
05/17/12
page 2 of 2
Inverses Practice For each function, on the same set of axes, sketch the graph of its inverse relation. Tell whether this inverse is also a function by writing YES or NO. 1) 2)
3)
4)
5) Restrict the domain of this quadratic function so that it is invertible. Then sketch the inverse function.
Domain restriction for y = f(x): ______________
©2012, TESCCC
05/17/12
Sketch y = f −1( x )
page 1 of 2
Precalculus HS Mathematics Unit: 02 Lesson: 02
Inverses Practice 6) Name an interval (domain) on which g (x ) would be invertible. Then sketch g −1( x ) on the same graph.
Domain restriction for g (x ) : ______________
s(t) 0 5 15 33 45 50 50 50
The given graph and table describe the function s(t), which gives the speed (s in mph) of an automobile as it accelerates over a period of 8 seconds (t).
60 50 Speed (mph)
t 0 1 2 3 5 6 7 8
40 30
7) Explain why s(t) is not invertible, but can be if the domain is restricted to [0, 6].
20 10 0
1
2
3 4 5 6 Time (seconds)
7
Let s −1(t ) represent the inverse function of s(t) (when its domain is restricted to [0, 6]). 8) Estimate the value of s(4). Explain what this means in the situation.
9) Estimate the value of s −1(25) and s −1(35) . Explain what these mean in the situation.
10) Sketch the graph of s −1(t ) on the grid provided. 11) Find the value of s −1(s(5)) . Explain what this means in the situation.
©2012, TESCCC
05/17/12
page 2 of 2
