Question

the y - intercept is 25. (simplify your answer. type an integer or a fraction.) (c) determine the zeros of the function and their multiplicity. use this information to determine whether the graph or touches the x - axis at each x - intercept. the zero(s) of f is/are - 1,5. (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed. type each an only once.) the lesser zero is a zero of multiplicity, so the graph of f the x - axis at x =. the greater zero is a z multiplicity, so the graph of f the x - axis at x =.

Explanation:

Step1: Recall zero - multiplicity rules

If a factor of a polynomial is of the form $(x - a)^n$, when $n$ is odd, the graph of the polynomial crosses the $x$-axis at $x = a$, and when $n$ is even, the graph touches the $x$-axis at $x=a$. Assume the function has factors $(x + 1)$ and $(x - 5)$ corresponding to the zeros $x=-1$ and $x = 5$.

Step2: Analyze the lesser zero

The lesser zero is $x=-1$. If we assume the factor corresponding to it is $(x + 1)$ (i.e., multiplicity $n = 1$, which is odd), the graph of $f$ crosses the $x$-axis at $x=-1$.

Step3: Analyze the greater zero

The greater zero is $x = 5$. If we assume the factor corresponding to it is $(x - 5)$ (i.e., multiplicity $n = 1$, which is odd), the graph of $f$ crosses the $x$-axis at $x = 5$.

Answer:

The lesser zero ($x=-1$) is a zero of multiplicity $1$, so the graph of $f$ crosses the $x$-axis at $x=-1$. The greater zero ($x = 5$) is a zero of multiplicity $1$, so the graph of $f$ crosses the $x$-axis at $x = 5$.