To graph the function y = 4(2^x) + 1, we can start by finding the y-intercept, which is the value of y when x = 0:
y = 4(2^0) + 1
y = 4(1) + 1
y = 5
Therefore, the y-intercept is (0, 5).
To find the domain of the function, we need to consider the base of the exponential function, which is 2^x. Since 2^x is defined for all real values of x, the domain of the function is all real numbers.
To find the range of the function, we can observe that the exponential function 2^x is always positive, so the minimum value of the function y = 4(2^x) is 4 times the minimum value of 2^x, which is 4(1) = 4. Therefore, the range of the function is y ≥ 4.
To graph the function, we can plot the y-intercept at (0, 5) and then plot a few more points for different values of x. For example:
When x = 1, y = 4(2^1) + 1 = 9, so we have the point (1, 9).
When x = -1, y = 4(2^-1) + 1 = 3, so we have the point (-1, 3).
Using these points, we can sketch the graph of the function as shown below:
graph of y=4(2^x)+1
Note that the graph never touches or crosses the x-axis, since 2^x is always positive.