Question

NO LINKS!! Please help me with these graphs Part 4a​

Answer 1

a. x = 1.75, x = 4.25

b. y = -7

c. Maximum point at (3, 5).

d. Domain: (-∞, ∞)

e. Range: (-∞, 5]

f. See attachment.

Explanation:

Given function:

`\text{f}(x)=-4|x-3|+5`

As per the question, use a graphing calculator to graph the given function.

Part a

The x-intercept(s) are the points at which the curve crosses the x-axis.

• x-intercepts: x = 1.75, x = 4.25

Part b

The y-intercept is the point at which the curve crosses the y-axis.

• y-intercept: y = -7

Part c

From inspection of the graph:

• Maximum point at (3, 5).

Part d

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

• Domain: (-∞, ∞)

Part e

The range of a function is the set of all possible output values (y-values).

As the function has a maximum point at y = 5, the range is restricted.

• Range: (-∞, 5]

Part f

Graph label the axes using a scale of 1 (see attachment).

• Plot the maximum point (3, 5).
• Plot the y-intercept: (0, -7).
• Draw a straight line from the maximum point through the y-intercept.

Substitute x = 5 into the function to find the value of y at that point:

`\begin{aligned}\implies \text{f}(5)&=-4|5-3|+5\\&=-4|2|+5\\&=-4(2)+5\\&=-8+5\\&=-3\end{aligned}`

• Plot found point (5, -3).
• Draw a straight line from the maximum point through point (5, -3).