(Q25.) Sample 3 GCC Math 101/120 Common Final Intermediate Algebra

TL;DR

Learn how to graph exponential equations by creating a table and plotting points on the coordinate plane.

Transcript

number 25 we are going to grab the equation white equal to 3 to the X minus 1 and we are going to make a table we're going to have five points then to the ground let's see our table will have three columns the first column will be 4x are you let's just put on X and the second color walking for Dwight value which we know why which is the equation it... Read More

Key Insights

• ❣️ Graphing exponential equations involves creating a table with x-values and calculating the corresponding y-values using the equation.
• ❎ Negative exponents in exponential equations are represented as fractions.
• 😵 The resulting graph of an exponential equation may touch the y-axis at the y-intercept but will never cross the x-axis.
• ❣️ The table and graph provide a visual representation of the relationship between x and y values in the equation.
• 6️⃣ Understanding the key points, such as y-intercepts and x-intercepts, is crucial for accurately graphing exponential equations.
• ☺️ The exponential equation graph shows exponential growth (or decay) as the x-values increase (or decrease).
• ❣️ The table helps to organize the calculation of y-values for different x-values.

Questions & Answers

Q: How do you create a table to graph an exponential equation?

To create a table, choose five x-values and calculate the corresponding y-values using the given equation. Then, label each point as positive, negative, or zero based on the value of y.

Q: What are the important points to consider when graphing exponential equations?

There are two key points to consider: the y-intercept and the presence of x-intercepts. In this case, the y-intercept is (0, 1/3). However, there are no x-intercepts in this particular equation.

Q: How do you deal with negative exponents in exponential equations?

Negative exponents in exponential equations are treated as fractions. In this equation, 3^-2 is equal to 1/3^2, which simplifies to 1/9. Similarly, 3^-3 becomes 1/3^3, resulting in 1/27.

Q: Can you explain how to plot the points on a graph for the given equation?

To plot the points, take the x-values from the table and locate the corresponding y-values on the graph. Connect the points with a smooth curve. The resulting graph should touch the y-axis at the y-intercept and never cross the x-axis.

Summary & Key Takeaways

• The video demonstrates how to graph the equation y = 3^x - 1 by creating a table with five points.

• The first column of the table represents the x-values, the second column represents the corresponding y-values, and the third column indicates the point's position (positive, negative, or zero).

• By plotting the points on a graph, the resulting exponential equation's graph is shown.