Questions: x 0 1 2 3 g(x) 8 10 25/2 125/8 C. An exponential function, f, with a y-intercept of 1.5 and a common ratio of 2. D. j(x)=3(1.6)^x

Transcript text: \begin{tabular}{|c|c|c|c|c|} \hline$x$ & 0 & 1 & 2 & 3 \\ \hline$g(x)$ & 8 & 10 & $\frac{25}{2}$ & $\frac{125}{8}$ \\ \hline \end{tabular} C. An exponential function, $f$, with a $y$-intercept of 1.5 and a common ratio of 2 . D. $j(x)=3(1.6)^{x}$

Solution

Solution Steps

Step 1: Analyze the graph

The graph appears to be an exponential function, as it starts low, close to the x-axis, and curves upwards quickly. It also seems to pass through the point (0, 4).

Step 2: Check table in option B

The table in option B does not represent an exponential function. The change in _g(x)_ is not consistent with a constant ratio. For example, from _x_ = 0 to _x_ = 1, _g(x)_ increases by 2 (10 - 8 = 2). From _x_ = 1 to _x_ = 2, _g(x)_ increases by 12.5 - 10 = 2.5.

Step 3: Check option C

The information in option C describes an exponential function of the form _f(x) = a_r^_x_ where 'a' is the y-intercept and 'r' is the common ratio. This would give _f(x) = 1.5 * 2_^_x_. This function passes through (0, 1.5), not (0,4), therefore it's not the graphed function.

Final Answer:

The correct answer must be D. j(x) = 3(1.6)ˣ. It is an exponential function. When x=0, j(x) = 3(1.6)⁰ = 3 * 1 = 3. When x is slightly less than 0, the function approaches the x-axis. When x is slightly greater than 0, the function grows. These properties align with the given graph. Therefore, the graph is most likely representing the exponential function j(x).

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