Question

1. determine if the function is increasing or decreasing and identify the intercepts.

a. increasing; x-intercept (-1,0) and y-intercept (0,-2)
b. increasing; x-intercept (0,-2) and y-intercept (-1,0)
c. decreasing; x-intercept (-1,0) and y-intercept (0,-2)
d. decreasing; x-intercept (0,-2) and y-intercept (-1,0)

1. identify the intercepts of the given function.

x	-24	-12	0	12	24
f(x)	-8	-6	-4	-2	0

a. x-intercept (0,12) and y-intercept (-6,0)
b. x-intercept (12,0) and y-intercept (0,-6)
c. x-intercept (0,24) and y-intercept (-4,0)
d. x-intercept (24,0) and y-intercept (0,-4)

Explanation:

Question 1

Step1: Analyze Function Trend

The graph's curve moves downward as \( x \) increases (from left to right), so the function is decreasing. Eliminate options a and b (which say "Increasing").

Step2: Identify Intercepts

• x - intercept: The point where the graph crosses the \( x \)-axis (where \( y = 0 \)). From the graph, this is \( (-1, 0) \).
• y - intercept: The point where the graph crosses the \( y \)-axis (where \( x = 0 \)). From the graph, this is \( (0, -2) \).

Check the remaining options (c and d). Option c matches the trend (Decreasing) and the intercepts. Option d has incorrect intercept labels (mixes \( x \) and \( y \) intercept definitions).

Step1: Recall Intercept Definitions

• x - intercept: Point where \( f(x)=0 \) (so \( y = 0 \)), format \((x, 0)\).
• y - intercept: Point where \( x = 0 \), format \((0, y)\) (where \( y = f(0) \)).

Step2: Analyze the Table

• From the table, when \( x = 24 \), \( f(x)=0 \). So the x - intercept is \((24, 0)\).
• When \( x = 0 \), \( f(x)= - 4 \). So the y - intercept is \((0, - 4)\).

Check the options: Option d matches these intercepts.

Answer:

c. Decreasing; x-intercept \((-1,0)\) and y-intercept \((0,-2)\)

Question 2