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Answer:
1. Behavior
The g(x) is large and positive when x is large and positive;
The g(x) is large and negative when x is large and negative.
2. y-intercept= -18
3. The zeros are: -3, -2 and 3
Step-by-step explanation:
1. End behavior:
To find this you have to know the leading coefficient of the variable with the highest degree, and whether the degree is even or odd.
(x + 3) = x positive, coefficient 1
(x + 2) = x positive, coefficient 1
(x − 3)= x positive, coefficient 1
The coefficient is 1*1*1= 1 = positive
There are 3 x, so it will be x^3= odd
The behavior for odd and positive will be:
g(x) is + ∞ when x=>+∞
g(x) is -∞ when x=>-∞
or
The g(x) is large and positive when x is large and positive;
The g(x) is large and negative when x is large and negative.
2. Y-intercept
The y-intercept is the value of y when the graph touches the y-axis. The y-axis is located at x=0, so to find the y-intercept you need to put x=0 on the graph function. Some graphs can have two y-intercepts but the graph on the question only has one. The calculation will be:
y-intercept = g(0)= (0+3)(0+2)(0-3)
y-intercept = 3*2*-3
y-intercept= -18
3. Zeros
The zeros mean the value of x that will result as g(x) as zero. At this coordinate, the graph will touch the x-axis since g(0) is located on the x-axis. That is why this coordinate also called an x-intercept. The function is expressed as the product of three things. If any of them is 0, then the result will be 0. So we have 3 zeros
+3=0
=-3
+2=0
=-2
-3=0
=3
The zeros are: -3, -2 and 3
Each ride has a fixed cost of 7 and a cost that increases proportionally to the distance travelled of 0.25 per mile. Therefore the total cost of the ride is:
Where "x" is the distance in miles. Marco can only spend 30 on his ride, therefore the cost must be less or equal to that value.
We can solve the linear equation by isolating the "x" variable on the left side.
Marco's travel must be shorter or equal to 92 miles.