Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - characteristics - Piecewise functions.
Test Yourself 1.


 

2 sections

Evaluate

 1. A function is defined as:

(i) What is the domain of f(x)?

(ii) What is the range of f(x)?

(iii) Evaluate 2f(4) - 3f(2).

Answer.(i) Domain is [0, 5].
(ii) Range is [-2, 9].
(iii) Value = 10.		 2. David defines a function he is using at work as:

(i) Evaluate f(2) + f(-2)

(ii) Draw a neat sketch of David's function.

(iii) What is the range of the function?

Answer.(i) 1.5.
(iii) Range is (0, 1].
 

3. A function is defined as

y = 2x

What is its domain and range?

 4.
Sketch. 5. Consider the following function:

(i) Find the value of f (-3).

(ii) Write down the value of f (a2).

(iii) Draw a sketch of the function
y = f(x) for the domain
-3 ≤ x ≤ 3.

  
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  9.  

3 sections

values.

11.

 

  
 

13.

 

 14.
Sketch. 15. A function is defined as:

(i) State the domain and range of the function.

(ii) Find the value of
f(-1) - f(1)

(iii) Draw a neat sketch of the function.

Answer.(i) D: All real x
R: y = -1 or y ≥ 0.
(ii) Value = -2.		 16. A function is defined as follows:

(i) Draw a neat sketch of the graph
y = f(x)

(ii) Evaluate f(2) + f(0) + f (-2)

Answer.(ii) 1.75.
  17. A function is defined as:

(i) Calculate f (-4).

(ii) Calculate f (-3).

(iii) Calculate f (k2).

(iv) Sketch the graph of y - f(x) over the domain -5 ≤ x ≤ 2 showing all essential features including intercepts on the axes.

18. A function is definedv as follows:

(i) Evaluate f (2).

(ii) Sketch the graph of the function in the given domain.

(iii) State the range of the function for this domain.
  19. 20.