Chapter 1, Problem 21PT

To determine

To identify: The whether the graph provided below is linear or not. Also compute and interpret the intercepts, symmetry, positive, negative, increasing, decreasing and the x -coordinate of any relative extrema and end the end behavior of the graph.

  

Answer to Problem 21PT

The graph is non-linear. The y -intercept $\left(0,0\right)$is andx -interceptis $\left(0,0\right)$. There is no symmetry. The graph is always positive. The graph is alwaysincreasing. There is no relative maximum and minimum. The end behavior of the graph is the number of gadgets sold keeps on increasing.

Explanation of Solution

Given information:

The graphical representation of number of number of gadgets sold in thousands over a period of time is provided below.

  

Formula used:

The graph of a function is said to be linear is it is straight line. If it is a curve it is non-linear.

The x- intercepts are the points on x -axis where the graph of the equation intersects the x -axis.

The y- intercepts are the points on y -axis where the graph of the equation intersects the y -axis.

When the graph of the function lies above the x -axis the function is said to be positive otherwise negative.

When the graph of the function goes up it is an increasing function when viewed from left to right otherwise function is decreasing.

The function has relative high and low values of function. A function has relative minimum when no other near by point has a lesser y -coordinate. A function has relative maximum when no other near by point has a greater y -coordinate.

End behavior of the graph represents the values of the function at positive and negative extremes in domain of the function.

Calculation:

Consider the graphical representation of number of number of gadgets sold in thousands over a period of time is provided below.

  

The x -axis denote the time in months and y -axis denote the number of gadgets sold in thousands.

Recall that the graph of a function is said to be linear is it is straight line. If it is a curve it is non-linear.

Observe that graph is not a straight line so it is a non-linear graph.

Also the graph of the function is not divided by any line into mirror images, so it is not symmetric also.

Recall that the x- intercepts are the points on x -axis where the graph of the equation intersects the x -axis.

Observe that the graph does intersect the x -axis at the origin so x- intercept is $\left(0,0\right)$ .

The y- intercepts are the points on y -axis where the graph of the equation intersects the y -axis.

Observe that the graph intersects the y -axis at the point $\left(0,0\right)$ that is number of gadgets sold initially were zero.

Recall that when the graph of the function lies above the x -axis the function is said to be positive otherwise negative.

Observe that graph of the function always lie above the x -axisso the function is said to be positive that is number of gadgets sold is always a positive number.

Recall that when the graph of the function goes up it is an increasing function when viewed from left to right otherwise function is decreasing.

The graph of the function is always increasing for $x>0$ that is number of gadgets sold increases with number of months.

Recall that the function has relative high and low values of function. A function has relative minimum when no other near by point has a lesser y -coordinate. A function has relative maximum when no other near by point has a greater y -coordinate.

There is neither relative maximum nor relative minimum.

Recall that the end behavior of the graph represents the values of the function at positive and negative extremes in domain of the function.

The graph describes the number gadgets sold. As the number of months increases the sale of gadgets also increases.