For the following graph:
a. Find the domain of f.
b. Find the range of f.
c. Find the x-intercepts.
d. Find the y-intercept.
e. Find the intervals over which f is increasing.
f. Find the intervals over which f is decreasing.
g. Find the intervals over which f is constant.
h. Find any points of discontinuity.
What graph?
To answer these questions about the graph, we need to visually analyze it. However, since we cannot see the actual graph, I'll explain how you can find the answers to each question by analyzing a graph.
a. To find the domain of f, look at the x-values on the graph. The domain of f is the set of all possible x-values for which f is defined. In other words, it is the set of all x-values where the graph exists. Typically, you can determine the domain by identifying any x-values where the graph is undefined, such as vertical asymptotes or points of discontinuity.
b. To find the range of f, look at the y-values on the graph. The range of f is the set of all possible y-values that correspond to the x-values within the domain. The range can be determined by identifying the highest and lowest points on the graph. If there are no restrictions or asymptotes, the range may be all real numbers or a specific interval.
c. To find the x-intercepts, look for the points on the graph where it crosses or touches the x-axis. These are the points where the y-value is zero, so setting f(x) equal to zero and solving for x will give you the x-intercepts.
d. To find the y-intercept, look for the point on the graph where it crosses or touches the y-axis. This is the point where the x-value is zero, so you can find the y-intercept by evaluating f(0).
e. To find the intervals over which f is increasing, look for portions of the graph where the slope is positive. This means that as you move from left to right, the graph is going up. The intervals of increasing can be found by identifying the regions where the graph is heading upwards.
f. To find the intervals over which f is decreasing, look for portions of the graph where the slope is negative. This means that as you move from left to right, the graph is going down. The intervals of decreasing can be found by identifying the regions where the graph is heading downwards.
g. To find the intervals over which f is constant, look for portions of the graph where the slope is zero. This means that as you move from left to right, the graph remains at a constant level. The intervals of constant can be found by identifying the regions where the graph is relatively flat.
h. To find any points of discontinuity, look for any vertical asymptotes or points where the graph has jump, hole, or vertical tangent. These points indicate that the function is not continuous at those specific x-values.
By analyzing the graph and applying these methods, you can find the answers to each of the questions about the graph.