Complete the following for f(x)=2^(x+1)-3
Range:
Coordinates of y-intercept:
To find the range of a function, we need to determine all possible values that the function can output for different inputs. In the case of the function f(x) = 2^(x+1) - 3, we can observe that the base of the exponential function is 2, which means the function will only output positive values or zero. This is because any positive number raised to any power will always result in a positive number.
Now, let's consider the minimum value that f(x) can take. Since the base of the exponential function is 2, the term 2^(x+1) will always be positive or zero, and subtracting 3 will still result in a value that is either positive or zero. Hence, the minimum value of f(x) is -3.
To find the range, we need to consider all values greater than or equal to -3. Therefore, the range of the function f(x) = 2^(x+1) - 3 is (-3, + ∞).
Moving on to the y-intercept, we know that the y-intercept occurs when x = 0. Therefore, substituting x = 0 into the equation f(x) = 2^(x+1) - 3, we can find the corresponding y-value.
f(0) = 2^(0+1) - 3
= 2^1 - 3
= 2 - 3
= -1
Therefore, the coordinates of the y-intercept are (0, -1).