Properties of Functions Practice

Question

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4 of 54 of 5 Items

Question
Use the image to answer the question.

A coordinate plane with four quadrants shows the x-axis ranging from negative 7 to 4 in increments of 1, and the y-axis ranging from negative 9 to 8 in increments of 1. An upward line with arrows at both the ends is shown on the plane. The line passes through the first, second, and third quadrants. The line intersects the x-axis at left parenthesis negative 1.5 comma 0 right parenthesis and the y-axis at left parenthesis 0 comma 3 right parenthesis.

Sekou sketched the graph shown based on a verbal description. Fill in the blanks to tell what information she was likely given.

(1 point)
The initial value of the function is
.
The function has a constant rate of change equal to
.

Answer 1

To analyze the information provided from Sekou's graph, we can determine the initial value and the constant rate of change based on the coordinates given.

1. Initial Value of the Function: The initial value is typically the y-intercept of the graph (the point where the graph intersects the y-axis). In the given scenario, the graph intersects the y-axis at the point (0, 3). Therefore, the initial value of the function is:

3.

2. Constant Rate of Change: The slope or rate of change of a linear function is calculated as the change in y divided by the change in x (rise over run). Based on the points provided:

• The line intersects the x-axis at (-1.5, 0) and the y-axis at (0, 3).

Using these points:

• Change in y (from y = 3 to y = 0) = 3 - 0 = 3.
• Change in x (from x = 0 to x = -1.5) = 0 - (-1.5) = 1.5.

So, the rate of change (slope) can be calculated as:

\[ \text{Rate of Change} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{3}{1.5} = 2. \]

Thus, the constant rate of change is:

2.

Putting it all together:

• The initial value of the function is 3.
• The function has a constant rate of change equal to 2.