Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph
f(x) = 5x - 3,lim x -->5 f(x)
To graph the function f(x) = 5x - 3, you can follow these steps:
1. Choose a range of x-values to plot on the graph. Let's say you choose x-values from -5 to 5.
2. Substitute each x-value into the function and calculate the corresponding y-value.
For example, when x = -5, y = (5 * -5) - 3 = -28.
3. Plot the points (x, y) on the graph using a coordinate plane.
4. Connect the plotted points with a straight line to obtain the graph of the function.
Now, to find the indicated limit, lim x --> 5 f(x), you need to examine the behavior of the graph as x approaches 5.
When x approaches 5 from the left side (x < 5), you can observe that the graph is approaching a single point on the line (5x - 3). The closer x gets to 5, the closer the y-values get to the corresponding value on the line.
Similarly, when x approaches 5 from the right side (x > 5), the graph also approaches the line as x gets closer to 5.
Therefore, the limit lim x --> 5 f(x) exists, and its value is the same as the y-coordinate of the point on the line where x = 5. By substituting x = 5 into the function, you can find the y-coordinate:
f(5) = (5 * 5) - 3 = 22.
Therefore, the limit lim x --> 5 f(x) is equal to 22.