# Graphing y=-3^x | Summary and Q&A

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November 22, 2016
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blackpenredpen
Graphing y=-3^x

## TL;DR

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

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### 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.