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

Exponential functions - Basic understanding and graphs.
Test Yourself 1.


 

 
Basic manipulation
(using index laws).		 1. Simplify (7x)4 - 3x. 2. Simplify .
  3. Expand . 4. Simplify (2 × 3x)×(3 × 2x)
  5. . 6. If f(x) = 2ex + 3e2x-1,

evaluate f(2) - f(0) leaving your answer in the simplest exact form.
Graphs. 7. Draw the graphs of

y = 3x and y = 5x

in the domain -2 ≤ x ≤ +2.

Compare the two curves.

 8. Sketch the graph of

y = ex + 3.

Describe the effect of the transformations made to the basic function.
  9. Sketch the graph of

y = 3 - 2e2x.

Describe the effect of the transformations made to the basic function.

 10. Sketch the graph of

y = 1 - 2e-x.

Describe the effect of the transformations made to the basic function.
  11. Sketch the graph of the catenary

in the domain -2 ≤ x ≤ +2.

Describe the shape of this curve.

 12. (i) Draw the graph of

y = e-x.

(ii) By drawing another graph on the same set of axes, show that

f(x) = e-x - x + 1

has exactly one root.
Equations reducible to quadratics. 13. Solve the equation

e2x - 28ex + 27 = 0

Leave your answer in exact form.

Answer.x = 3loge3 or x = 0.		 14. Solve the following equation

2e2x - ex = 0

Answer.x = - ln 2.
  15. Solve the following equation

e2x+ 3ex - 10 = 0.

Answer.x = loge 2.		 16. Show that the only solution to the equation

4e3x - e2x = 0

is x = -2ln2.