Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 21–28, the graph of a function is given. Use the graph to find:

(a) The intercepts, if any

(b) The domain and range

(c) The intervals on which it is increasing, decreasing, or constant

(d) Whether it is even, odd, or neither

Step-by-Step Solution

Answer

1. The intercepts are, $\left(0,1\right)$.
2. The domain of the function of the given graph is, the set of all the real numbers and the range is, $\left\{y|0\le y\le \infty \right\}$.
3. The graph is increasing on the interval $\left(-\infty ,\infty \right)$ and the graph is not decreasing at any points and not constant at any points.
4. The function of the given graph is neither even nor odd.

Part a Step 1 . Given information

The graph touches the y-axis at $\left(0,1\right)$.

Part b Step 1 . Find the domain and the range.

The domain of the function of the given graph is, the set of all the real numbers.

The graph have $y$ coordinates between $0$ and $\infty$. So, the range of $y$ is, $\left\{y|0\le y\le \infty \right\}$.

Part c Step 1 . Determine the intervals on which it is increasing, decreasing, or constant.

The graph is increasing on the interval $\left(-\infty ,\infty \right)$.

The graph is not decreasing, as the function $f$ is not decreasing at any points on the graph.

The function $f$ is not constant at any points on the graph.

Part d Step 1 . Find Whether the graph of a function is even, odd, or neither.

From the graph we can see that, for a point $\left(x,y\right)$ there is no point $\left(-x,y\right)$ or $\left(-x,-y\right)$ on the graph.

So, the given graph is not symmetric with respect to the $y$-axis or the origin.

Therefore, the function is neither even nor odd.