Explain why the solution to the absolute value inequality |4x-9|>-12 is all real numbers
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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