Unit 1.1.1 (a) Function
1. (a) Define linear function with example.
Solution:
If a function can be expressed as , Where and are constants, then the function is called linear function.
1. (b) What is the coordinates of vertex of
Solution:
The vertex of is
1. (c) Identify the identity function: and
Solution: Identity function is .
2. (a) Study the following graphs and identitify their nature as identity, constant, quadratic and cubic function.
Solution:
This is a graph of constant function.
This is a graph of identity function.
This is a graph of cubic function.
This is a graph of quadratic function.
This is a graph of cubic function
This is a graph of quadratic function.
3. (a) Draw the graph of
Solution:
Given,
Therefore, passing points are (1,3),(2,4) and (3,5).
3. (b) Draw the graph of
Solution:
Here represents the horizontal line passing through (0,6) .
3. (c) Draw the graph of
Solution:
Given,
Hence passing points are (-3,9), (-2,4), (-1,1), (0,0), (1,1), (2,4) and (3,9).
3. (d) Draw the graph of
Solution:
Given,
Hence, the passing points are (-3,-9), (-2,-4), (-1,-1), (0,0), (1,-1), (2,-4) and (3,-9).
3. (e) Draw graph of
Solution:
Given,
Now,
4. Pemba estimates the minimum ideal weight of a woman, in pounds is to multiply her height, in inches by 4 and subtract 130. Let y = minimum ideal weight and x = height.
(a) Express y as a linear function of x.
Solution:
(b) Find the minimum ideal weight of a woman whose height is 62 inches.
Solution:
Here,
(c) Draw the graph of height and weight
Solution:
Here,
We have,
5. Investigate the nature of graph showing linear, quadratic and cubic function in our daily life. Make a report and present it in classroom.
This is a graph of constant function.
This is a graph of identity function.
This is a graph of cubic function.
This is a graph of quadratic function.
This is a graph of cubic function
This is a graph of quadratic function.
3. (a) Draw the graph of
Solution:
Given,
Therefore, passing points are (1,3),(2,4) and (3,5).
3. (b) Draw the graph of
Solution:
Here represents the horizontal line passing through (0,6) .
3. (c) Draw the graph of
Solution:
Given,
Hence passing points are (-3,9), (-2,4), (-1,1), (0,0), (1,1), (2,4) and (3,9).
3. (d) Draw the graph of
Solution:
Given,
Hence, the passing points are (-3,-9), (-2,-4), (-1,-1), (0,0), (1,-1), (2,-4) and (3,-9).
3. (e) Draw graph of
Solution:
Given,
Now,
4. Pemba estimates the minimum ideal weight of a woman, in pounds is to multiply her height, in inches by 4 and subtract 130. Let y = minimum ideal weight and x = height.
(a) Express y as a linear function of x.
Solution:
(b) Find the minimum ideal weight of a woman whose height is 62 inches.
Solution:
Here,
(c) Draw the graph of height and weight
Solution:
Here,
We have,
5. Investigate the nature of graph showing linear, quadratic and cubic function in our daily life. Make a report and present it in classroom.