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Sagot :
Statements that describe the given function are:
- (A) f(x) has one real zero because it crosses the x-axis once.
- (D) f(x) has a real zero at 2.5.
- (G) f(x) has an x-intercept at (2.5, 0).
What is a function?
- A function from a set X to a set Y allocates exactly one element of Y to each element of X.
- The set X is known as the function's domain, while the set Y is known as the function's codomain.
To find the statements that describe the given function:
- The following function can be reorganized: [tex]f(x)=\frac{2*x-5}{2*(x-1)*(x+1)}[/tex]
- There is one real zero (numerator) in the function (x-intercept), which is x = 2.5.
- Besides, x = 1 and x = -1 are poles (denominator), that is, x-values so that function is undefined.
Lastly, the correct answers are:
- (A) f(x) has one real zero because it crosses the x-axis once.
- (D) f(x) has a real zero at 2.5.
- (G) f(x) has an x-intercept at (2.5, 0).
Therefore, statements that describe the given function are:
- (A) f(x) has one real zero because it crosses the x-axis once.
- (D) f(x) has a real zero at 2.5.
- (G) f(x) has an x-intercept at (2.5, 0).
Know more about functions here:
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The complete question is given below:
Which statements describe the function f(x)=2x-5/2(x^2-1)? Check all that apply.
(A) f(x) has one real zero because it crosses the x-axis once.
(B) f(x) has two real zeros because it crosses the x-axis twice.
(C) f(x) has real zeros at 1 and –1.
(D) f(x) has a real zero at 2.5.
(E) f(x) has x-intercepts at (1, 0) and (–1, 0).
(F) f(x) crosses the x-axis when x = 1 and x = –1.
(G) f(x) has an x-intercept at (2.5, 0).
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