Suppose $f(x)=x^{2}+8 x+15$. Which of the following is not true? $f(x) \rightarrow \infty$ as $x \rightarrow \infty$ $f$ has a horizontal intercept at $x=-3$. $f$ has a horizontal intercept at $x=15$ $f$ has a horizontal intercept at $x=-5$. $f$ has a vertical intercept at $y=15$

Step 1 ：Given the function \(f(x) = x^{2} + 8x + 15\), we are asked to determine which of the following statements is not true.

Step 2 ：The first statement, \(f(x) \rightarrow \infty\) as \(x \rightarrow \infty\), is true because as x approaches infinity, the value of the function also approaches infinity due to the \(x^{2}\) term.

Step 3 ：The function \(f(x) = x^{2} + 8x + 15\) is a quadratic function and its roots can be found using the quadratic formula. The roots of the function are the x-values where the function intersects the x-axis (horizontal intercepts).

Step 4 ：The vertical intercept of a function is the y-value where the function intersects the y-axis. This occurs when x = 0.

Step 5 ：Let's calculate the roots and the vertical intercept of the function to determine which of the statements are not true.

Step 6 ：The roots of the function are -5 and -3, which means the function has horizontal intercepts at \(x = -5\) and \(x = -3\). The function does not have a horizontal intercept at \(x = 15\). The vertical intercept of the function is 15.

Step 7 ：Therefore, the statement \(f\) has a horizontal intercept at \(x=15\) is not true.

Step 8 ：\(\boxed{\text{Final Answer: } f\text{ has a horizontal intercept at } x=15 \text{ is not true.}}\)