Answer :
Final answer:
To determine the correct formula for a straight-line graph, the slope and y-intercept need to be evaluated. Graphs of exponential functions can be plotted by computing points for each equation and joining them. Examining the direction of the slope and the y-intercept will aid in matching the graph to the correct formula.
Explanation:
To graph the function and determine the correct formula for the graph shown, we need to consider two components: the slope and the y-intercept. The slope of a line indicates how steep the line is and is calculated as the rise over run. The y-intercept is the point where the line crosses the y-axis. To distinguish between the formulas y = -x - 1 and y = x + 1, we would look at the slope and y-intercept of the graph provided, assuming it displayed a straight line.
For example, if the slope is negative, the line will slope downwards from left to right, which would match the formula y = -x - 1. If the slope is positive, the line will slope upwards, corresponding to y = x + 1. In any case, we will also check the y-intercept to verify that it matches the constant term in the equation.
If the graph is not a straight line, such as a curve representing exponential growth or decay, we would compare to the functions y = e^x, y = e^{-x}, y = x^2, or y = -x^2 for example. To graph these correctly on the same diagram, we would plot a series of points for each equation and connect them to illustrate the shape of the curve.
