base e assignment active practice graphing exponential functions in base e. identify the graph of y = e^x - 2.
base e assignment active practice graphing exponential functions in base e. identify the graph of y = e^x - 2.
Answer
Explanation:
Step1: Analyze key - points of the function
The parent function of (y = e^{x}-2) is (y = e^{x}). The graph of (y = e^{x}) has a (y) - intercept at ((0,1)) and is an increasing function. For (y = e^{x}-2), we use the vertical - shift rule. When we have (y=f(x)+k), if (k=- 2), the graph of (y = f(x)) is shifted down by 2 units. So the (y) - intercept of (y = e^{x}-2) is ((0,1 - 2)=(0,-1)) and it is still an increasing function.
Step2: Match with the graphs
We look for a graph that is an increasing exponential curve and has a (y) - intercept at ((0,-1)).
Answer:
The graph that is an increasing exponential function with a (y) - intercept at ((0,-1)) (you need to visually identify this among the given graphs in the image).