Starting with the graph of \( f(x)=5^{x} \), write the equation of the graph that results when: (a) \( f(x) \) is shifted 3 units upward. \( y= \) (b) \( f(x) \) is shifted 3 units to the left. \( y= \) (c) \( f(x) \) is reflected about the \( x \)-axis and the \( y \)-axis. \( y= \)

To modify the function \( f(x) = 5^x \) according to the specified transformations, we can apply the following rules: (a) **Shift 3 units upward**: To shift a function upward by \( k \) units, we add \( k \) to the function. Therefore, shifting \( f(x) \) upward by 3 units gives us: \[ y = f(x) + 3 = 5^x + 3 \] (b) **Shift 3 units to the left**: To shift a function to the left by \( h \) units, we replace \( x \) with \( x + h \). Thus, shifting \( f(x) \) to the left by 3 units results in: \[ y = f(x + 3) = 5^{x + 3} \] (c) **Reflect about the \( x \)-axis and the \( y \)-axis**: Reflecting a function about the \( x \)-axis involves multiplying the function by -1, and reflecting about the \( y \)-axis involves replacing \( x \) with \( -x \). Therefore, reflecting \( f(x) \) about both axes gives us: \[ y = -f(-x) = -5^{-x} \] In summary, the equations for the transformations are: (a) \( y = 5^x + 3 \) (b) \( y = 5^{x + 3} \) (c) \( y = -5^{-x} \)