If you subtracted 3 from the exponent in an exponential function, what would happen to the graph?
A) It would move up 3
B) It would move down 3
C) It would move to the left 3
D) It would move to the right 3
You don't have to be rude when you say no help from yall
it only took you 20 minutes, so maybe you didn't need to come here at all.
Still, good work.
Brady Sneed
just now
To understand what would happen to the graph if you subtracted 3 from the exponent in an exponential function, let's start by understanding the general form of an exponential function:
y = a * b^x,
where
- y represents the dependent variable (often the vertical axis)
- a is a constant representing the initial value or the value of y when x = 0
- b is a constant greater than 0 and not equal to 1, known as the base of the exponential function
- x is the independent variable (often the horizontal axis)
Now, if we subtract 3 from the exponent, our new exponential function would be:
y = a * b^(x - 3).
To determine what would happen to the graph, we can compare this new function to the original exponential function.
In the original exponential function, y = a * b^x, the value of x determines the rate at which y changes. As x increases, the value of y grows more rapidly if the base, b, is greater than 1, or decays more rapidly if b is between 0 and 1.
When we subtract 3 from x in the new function, y = a * b^(x - 3), it means the value of x is effectively shifted to the right by 3 units. Recall that subtraction moves values to the right on the number line. Consequently, the graph of the new function will be shifted to the right by 3 units.
Therefore, the correct answer is D) It would move to the right 3.