Graphing y=-3^x

TL;DR

This content explains how to graph the exponential function y = -3^x using a table of values.

Transcript

in this question will be graphing the equation why it's equal to negative 3 to the X power and you see that there's no parentheses the X power right here it's only good for the numbers 3 & 2 graph this I will show you get with the table so let's first make a table with 5 points I will pick some X values and the y value will be negative 3 and that g... Read More

Key Insights

• ❣️ Graphing the exponential function y = -3^x requires creating a table of values and substituting x values into the equation.
• 😵 The graph of y = -3^x is a curve that never crosses the x-axis.
• ❣️ Positive x values result in negative y values, and as x values decrease, y values approach zero but never reach it.
• 🟰 The exponential function y = -3^x is always negative and never equal to zero or positive.
• 😀 The graph of y = -3^x can be reflected but will always maintain its shape.
• 👈 Selecting different x values allows us to plot points and visualize the exponential curve.
• ❣️ The curve of y = -3^x is steeper as x values become more negative.

Questions & Answers

Q: How do you graph the exponential function y = -3^x without using parentheses or additional terms?

To graph y = -3^x, create a table of values by selecting different x values. Substitute each x value into the equation to obtain the corresponding y values. Plot these points on a graph and connect them to visualize the curve.

Q: What is the significance of selecting x = 0 as the first value in the table?

Selecting x = 0 as the first value allows us to determine the y value when x is not negative. In this case, when x = 0, y = -1. This value helps establish a reference point on the graph.

Q: Why does the graph of y = -3^x never cross the x-axis?

The graph never crosses the x-axis because the exponential function -3^x can never be equal to zero. Regardless of the value of x chosen, the y value will always be negative and unequal to zero.

Q: How does the graph change when negative x values are used in the table?

When negative x values are used, the y values will still be negative and decrease as x becomes more negative. The curve will approach the x-axis but never intersect it.

Summary & Key Takeaways

• The content demonstrates how to create a table of values for the exponential function y = -3^x.

• By selecting various x values and using the given equation, the corresponding y values are calculated.

• Graphing the points from the table reveals the shape of the graph, which shows that the curve never crosses the x-axis.