Rational Functions Unit Online Practice Complete this assessment to review what you've learned. It will not count toward your grade. The graph of the function \( f(x)=\frac{1}{x} \) is horizontally stretched by a factor of 15 when it is replaced by \( g(x) \). Which of the following is the expression o \( g(x) \) ? (1 point) \( g(x)=\frac{1}{x+15} \) \( g(x)=\frac{1}{15 x} \) \( g(x)=\frac{1}{\frac{1}{x} x} \) \( g(x)=\frac{1}{x-15} \) Incorrect

When dealing with the horizontal stretch of a function, you can think about how the variable in the function is manipulated. For a stretch by a factor of \( k \), you replace \( x \) with \( \frac{x}{k} \). In this case, since the stretch factor is 15, the function will change from \( f(x) \) to \( g(x) = f\left(\frac{x}{15}\right) \). Therefore, the correct expression for \( g(x) \) is \( g(x) = \frac{1}{\frac{x}{15}} = \frac{15}{x} \), which is not listed in your options but crucial for understanding stretches! Additionally, when you manipulate rational functions such as \( f(x) \) and \( g(x) \), it’s essential to remember that horizontal transformations occur inside the function. It’s often easy to confuse horizontal and vertical stretches—always check whether you’re dividing or multiplying the \( x \) variable! Keep practicing by altering different functions, and soon these concepts will feel like second nature!