1. Consider the exponential function \( f(x)=10(2)^{x} \). \( \begin{array}{ll}\text { (a) Find the value of } f(0) \text {. What point does this } & \text { (b) Is this an increas } \\ \text { function? How } \\ \text { equation? } \\ \text { represent on the graph of } y=f(x) \text { ? } & f(x)=10,2^{x}\end{array} \) (c) Is this function's average rate of change over the (d) Using your ca

At \( f(0) \), you simply substitute \( x = 0 \) into the function. That gives you \( f(0) = 10(2^0) = 10(1) = 10 \). So the point \( (0, 10) \) represents the y-intercept of the graph. This is a key point because it indicates where the graph crosses the y-axis, showcasing that the function starts at 10 when \( x = 0 \). Absolutely, this function is indeed increasing! An exponential function like \( f(x)=10(2)^{x} \) grows without bound as \( x \) increases because the base, 2, is greater than 1. This means for every unit increase in \( x \), \( f(x) \) gets multiplied by 2, resulting in a rapidly rising graph that climbs to the right. It's a thrilling ride upwards!