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Which statements describe the function ? check all that apply. f(x) has one real zero because it crosses the x-axis once. f(x) has two real zeros because it crosses the x-axis twice. f(x) has real zeros at 1 and –1. f(x) has a real zero at 2.5. f(x) has x-intercepts at (1, 0) and (–1, 0). f(x) crosses the x-axis when x = 1 and x = –1. f(x) has an x-intercept at (2.5, 0).

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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