SOLUTION: What are the domain and range for the function f(x)=4(2^(2x)+3)-7?

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Question 1090677: What are the domain and range for the function f(x)=4(2^(2x)+3)-7?
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
Domain: All real numbers
Range: (5, infinity)

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Another response from tutor @CubeyThePenguin that is of no use to the student, since it teaches the student nothing....

The function is an increasing exponential function.

Domain: an exponential function can be evaluated for any input value, so the domain is all real numbers.

Range: an increasing exponential function has a minimum value but no maximum value.

2^(2x) has no minimum value; it gets as close as we want to 0 for large negative values of x. So...

The range of 2^(2x) is (0,infinity); the y-intercept is 1

graph%28400%2C400%2C-2%2C2%2C-2%2C20%2C2%5E%282x%29%29

The +3 raises the graph up 2 units; the range of 2^(2x)+3 is (3, infinity); the y-intercept is 1+3=4

graph%28400%2C400%2C-2%2C2%2C-2%2C20%2C2%5E%282x%29%2C2%5E%282x%29%2B3%29

Multiplying by 4 stretches the graph vertically by a factor of 4; the range of 4(2^(2x)+3) is (12, infinity); the y-intercept is 4(4) = 16



The "-7" moves the graph down by 7; the range of 4(2^(2x)+3)-7 is (5, infinity); the y-intercept is 16-7=9



The range of the function is (5, infinity)