Horizontal Scaling F19040

1. The problem is to understand how to multiply or scale a graph horizontally. 2. The general formula for horizontal scaling of a function $f(x)$ is given by $g(x) = f(bx)$, where $b$ is the horizontal scaling factor. 3. Important rule: If $|b| > 1$, the graph compresses horizontally (gets narrower). 4. If $0 < |b| < 1$, the graph stretches horizontally (gets wider). 5. For example, if $f(x) = x^2$, then $g(x) = f(2x) = (2x)^2 = 4x^2$ compresses the graph horizontally by a factor of 2. 6. Conversely, $g(x) = f(\frac{1}{2}x) = (\frac{1}{2}x)^2 = \frac{1}{4}x^2$ stretches the graph horizontally by a factor of 2. 7. Remember, the horizontal scaling affects the input variable $x$ inside the function, not the output. Final answer: To multiply a graph horizontally by a factor $b$, replace $x$ with $bx$ in the function, i.e., use $g(x) = f(bx)$.