Question

question 1 1 pts suppose the value x = 5 is a zero of a function f(x). what does this mean? f(5)=0 all of these answer choices describe what it means for x = 5 to be a zero of f(x) there is a horizontal intercept at x = 5 the point (5, 0) is on the graph of f(x). question 2 1 pts given h(x)=-3(x + 4)(x - 1), what are the zeros of the function? - 4 and 1 4 and - 1 4 and - 1 and - 3 - 4 and 1 and - 3 question 3 1 pts if the zeros of a function g(x) are - 7 and 3, which of the following could be a possible formula for g(x)? g(x)=-2(x + 7)(x - 3) g(x)=-7(x + 3) g(x)=-2(x + 7)(x + 3) g(x)=-7

Explanation:

Question 1

Step1: Definition of zero of a function

A zero of a function \(y = f(x)\) is a value of \(x\) such that \(f(x)=0\). When \(x = 5\) is a zero of \(f(x)\), \(f(5)=0\). Also, the \(x\) - intercepts of the graph of \(y = f(x)\) are the values of \(x\) for which \(y = 0\), so there is a horizontal ( \(x\) - axis) intercept at \(x = 5\) and the point \((5,0)\) lies on the graph of \(f(x)\).

Question 2

Step1: Set the function equal to zero

Set \(h(x)=-3(a + 4)(a - 1)=0\). By the zero - product property, if \(AB = 0\), then either \(A = 0\) or \(B=0\). So \(a+4 = 0\) gives \(a=-4\) and \(a - 1=0\) gives \(a = 1\).

Question 3

Step1: Use the zero - factor form

If the zeros of a function \(g(x)\) are \(x=-7\) and \(x = 3\), then the function can be written in the form \(g(x)=k(x+7)(x - 3)\) where \(k\) is a non - zero constant. Here \(k=-2\) in the option \(g(x)=-2(x + 7)(x - 3)\).

Answer:

Question 1: B. ALL of these answer choices describe what it means for \(x = 5\) to be a zero of \(f(x)\)
Question 2: A. - 4 and 1
Question 3: A. \(g(x)=-2(x + 7)(x - 3)\)