domain of exponential function from y axis & logarithmic function from x axis?
To determine the domain of an exponential function from the y-axis or a logarithmic function from the x-axis, we need to consider the restrictions or limitations on the input values.
For an exponential function, remember that it has the general form y = a * b^x, where 'a' is a constant and 'b' is the base.
- If we are considering the domain of the exponential function from the y-axis, it means we are looking at the values of 'y' (the output) to determine the restrictions on 'x' (the input). In this case, there are usually no restrictions on the domain since 'y' can take any value.
So, the domain of the exponential function from the y-axis is all real numbers, (-∞, +∞).
For a logarithmic function, it has the general form y = log_b(x), where 'b' is the base.
- If we are considering the domain of the logarithmic function from the x-axis, it means we are looking at the values of 'x' (the input) to determine the restrictions on 'y' (the output). In this case, the domain is restricted by the fact that the argument (x) of the logarithm must be greater than zero: x > 0.
So, the domain of the logarithmic function from the x-axis is all positive real numbers, (0, +∞).