Starting with the graph of a basic function, graph the following function using the techniques of shifting, compressing, stretch
ing, and/or reflecting. Find the domain and range of the function. f(x) = -(x + 1)3-1
1 answer:
Answer:
Domain and range of the function is all real number.
Step-by-step explanation:
The given function is
.... (1)
It is a cubic function.
The parent cubic function is
The translation is defined as
.... (2)
where, k is stretch factor, a is horizontal shift and b is vertical shift.
If |k|>1, then the graph of g(x) stretch by factor k and if 0<|k|<1
, then the graph of g(x) compressed by factor k. If k<0, then graph of g(x) reflects across x-axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2), we get
k=-1<0, so the graph reflects across x-axis.
a=1>0, so the graph of parent function shifts 1 units left.
b=-1<0, so the graph of parent function shifts 1 units down.
Domain and range of cubic polynomial is all real number. Since the given function is a cubic polynomial, therefore domain and range of the function is all real number.
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The limits match, so is continuous.
For the others: Each of the individual pieces of are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
The value of x is –7.
Solution:
Given expression:
Let us factor .
Substitute this in the fraction.
To make the denominator same, multiply and divide the first term by (x +1).
Denominators are same, you can add the fractions.
Cancel the common term in the numerator and denominator.
Multiply the fractions.
The expression is simplified to one rational expression.
Suppose the expression is equal to 0.
Do cross multiplication.
Any number or variable multiplied by 0 gives 0.
Subtract 7 from both sides of the equation.
x = –7
The value of x is –7.