Determine the parent function from which the graph of the function shown below can be otained. Next identify each transformation that can be applied to the parent function in order to obtain the graph of the function shown below. \[ f(x)=7^{x}-2 \] a) Choose the correct parent function. $y=7^{x}$ $y=\left(\frac{1}{7}\right)^{x}$ $y=\log _{7}(x)$ $y=\log _{\frac{1}{7}}(x)$ b) Choose the correct transformation (Reflections). Select an answer c) Choose the correct transformation (Stretches/Compressions). Select an answer d) Choose the correct transformation (Vertical Shifts). Select an answer e) Choose the correct transformation (Horizontal Shifts). Select an answer Submit Question Jump to Answer

Step 1 ：The parent function is the simplest form of the given function. In this case, the parent function is \(y=7^{x}\), because the given function \(f(x)=7^{x}-2\) can be obtained by applying transformations to the parent function \(y=7^{x}\).

Step 2 ：The transformations applied to the parent function to obtain the given function are as follows:

Step 3 ：There is no reflection because the function \(f(x)=7^{x}-2\) is not reflected across the x-axis or the y-axis.

Step 4 ：There is no stretch or compression because the base of the exponent (7) and the exponent (x) in the function \(f(x)=7^{x}-2\) are the same as in the parent function \(y=7^{x}\).

Step 5 ：There is a vertical shift of 2 units down because the function \(f(x)=7^{x}-2\) is obtained by subtracting 2 from the parent function \(y=7^{x}\).

Step 6 ：There is no horizontal shift because the function \(f(x)=7^{x}-2\) is not shifted to the left or right of the parent function \(y=7^{x}\).

Step 7 ：Final Answer: \(\boxed{a)}\) The correct parent function is \(y=7^{x}\). \(\boxed{b)}\) There is no reflection. \(\boxed{c)}\) There is no stretch or compression. \(\boxed{d)}\) The correct vertical shift is 2 units down. \(\boxed{e)}\) There is no horizontal shift.