Given \( f(x)=2 x-4 \), describe how the value of \( k \) affects the slope and \( y \)-intercept of the graph of \( g \) compared to the graph of L . \[ g(x)=2(x+15)-4 \] Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice (Type integers or simplified fractions ) A. The slope is scaled by a lactor of \( \square \) . and the \( y \)-ntercept is unchanged. B. The slope is unchanged, and the \( y \)-intercept is shifted down by \( \square \) unit(s) C. The slope is unchanged, and the \( y \)-intercept is shifted up by \( \square \) unit(s) D. The slope and \( y \)-intercept are both changed. The slope is scaled by a lactor of \( \square \) , and the \( y \)-intercept is scaled by a factor of \( \square \) E. The slope and the \( y \)-intercept are both unchanged Help me solve this View an example Get more help - Clear all Check answar
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To analyze the relationship between the functions \( f(x) = 2x - 4 \) and \( g(x) = 2(x + 15) - 4 \), we can start by rewriting \( g(x) \). By using the distributive property: \[ g(x) = 2(x + 15) - 4 = 2x + 30 - 4 = 2x + 26 \] Now, let's compare the two functions: 1. The slope of both lines is \( 2 \). This means the slope is unchanged. 2. The \( y \)-intercept of \( f(x) \) is \( -4 \), whereas the \( y \)-intercept of \( g(x) \) is \( 26 \). This indicates that the \( y \)-intercept is shifted up. So, we can fill in the answer choices: - The slope is unchanged. - The \( y \)-intercept is shifted up by \( 30 \) units (from -4 to 26). The correct choice is: C. The slope is unchanged, and the \( y \)-intercept is shifted up by \( 30 \) unit(s).
