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

Advanced functions - transformations.
Test Yourself 1.


 

On this page, questions relate to Exponential, Logarithmic and Trigonometric functions.

Exponential. 1. A function is defined as f(x) = 2x + 1.

(i) Sketch this function.

(ii) Sketch the function when it is reflected about the y axis - so g(x) = f(-x).

(iii) Sketch the function when the original function is reflected about the x axis -
so h(x) = -f(x).

(iv) Sketch the function k(x) = -f(-x).
  2.
   
   
  5.
Logarithmic. 6. The function y = ln x is transformed by:
  • being dilated vertically by a scale factor of 3;
  • then translated horizontally 4 units to the left.

Find the equation of the transformed function.

Answer.y = 3 ln(x+4).
 

7. (i) Sketch the function f(x) = ln (x) +1.

Sketch the graphs resulting from applying each of the following transformations to f(x). Also write a short statement describing what has changed from the original graph.

(i) g(x) = f(-x) -1.

(ii) h(x) = f(2x)

(iii) k(x) = 2f(x) + 1.
  8.
  9.
  10.
Trigonometric. 11.
   
   
   
  15.
Basic function. 16.