Math Lesson 15.5.3 - Plotting Exponential Graphs

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Welcome to our Math lesson on Plotting Exponential Graphs, this is the third lesson of our suite of math lessons covering the topic of Exponential Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Plotting Exponential Graphs

As in other cases, we can plot the graph of an exponential function by giving some values to the variable x and finding the corresponding y-values. In this way, we obtain a number of points on the graph, which when connected smoothly give the graph's shape. In exponential functions, it is better to take an odd number of values that have a certain symmetry in distribution. We said odd because we also take into consideration x = 0. For example, we take the values of x from -4 to 4 with an increment step of 1 unit and calculate the corresponding y-values, such as in the example below.

Example 3

1. Plot the graph of the exponential function
   y(x) = 5 ∙ 2^x-1
2. Find the horizontal asymptote of the graph.

Solution 3

1. Let's make the table we were referring to. Here we can take for the variable the values from -3 to 3 including 0. In this way, we have obtained the following points of the given exponential graph: A(-3, -3/8), B(-2, 1/4), C(-1, 3/2), D(0, 4), E(1, 9), F(2, 19) and G(3, 39). Inserting all these points into the coordinates system and connecting them smoothly yields the following graph:
2. The (horizontal) asymptote of the graph is obtained by trying to calculate the minimum of the function. Thus, since the exponential term 2^x cannot be negative, its minimum value is zero (for x points towards minus infinity) and will also be when this term is multiplied by 5. Therefore, the value of the asymptote is determined by the constant t, which in this case is -1. Therefore, y = -1 is a horizontal asymptote for this graph, as t = -1.

You have reached the end of Math lesson 15.5.3 Plotting Exponential Graphs. There are 8 lessons in this physics tutorial covering Exponential Graphs, you can access all the lessons from this tutorial below.

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2. Types of Graphs Math tutorial: Exponential Graphs. Read the Exponential Graphs math tutorial and build your math knowledge of Types of Graphs
3. Types of Graphs Revision Notes: Exponential Graphs. Print the notes so you can revise the key points covered in the math tutorial for Exponential Graphs
4. Types of Graphs Practice Questions: Exponential Graphs. Test and improve your knowledge of Exponential Graphs with example questins and answers
5. Check your calculations for Types of Graphs questions with our excellent Types of Graphs calculators which contain full equations and calculations clearly displayed line by line. See the Types of Graphs Calculators by iCalculator™ below.
6. Continuing learning types of graphs - read our next math tutorial: Circle Graphs

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