exponential basics
What is the general form of an exponential function?
What is f(x)=a⋅b^x
What is the horizontal asymptote of f(x)=2^x
What is Y=0
What transformation occurs when adding 3 to f(x)=2^x, resulting in f(x)=2^x+3?
What is a vertical shift of 3 units
For f (x) = e^−x + 1, find functions g and h so that f = g + h.
What are f(x)=e^-x and g(x)=1
In an exponential function f(x)=a⋅b^x, if b>1, does the graph increase or decrease
What is increase
True or False: The range of any exponential function f(x)=b^x where b>0 is (0,∞)
What is true
How does the graph of f(x)=2^(x−2) compare to the graph of f(x)=2^x
What is a shift to the right by 2 units?
For f(x)=2e^x−5, find functions g and h so that f=g−h.
What are f(x)=2e^x amd g(x)=5
For the function f(x)=2^x, what is the y-intercept?
What is (0,1)
As x approaches negative infinity for f(x)=2^x, what does f(x) approach?
What is 0
What transformation results from f(x)=−2^x?
What is a reflection over the x-axis?
For k (x) = e^-x^2 find functions f and g so that k = g ◦f
What are f(x) = −x^2 and g(x) = e^x
What is the domain of any exponential function?
What is all real numbers
For f(x)=−2^x, what is the range?
What is (−∞,0)?
If f(x)=b^x and b<1,as x approach’s negative infinity, f(x) approaches?
What is infinity
For f (t) = t^2e^−t , find functions g and h so that f = gh
What are g(t) = t^2 and h(t) = e^−t
If f(x)=3⋅0.5^x, is this function increasing or decreasing?
What is decreasing
Identify the asymptote of the function f(x)=3⋅(2^x)−4
What is y=-4
Describe the transformation from f(x)=2^x to f(x)=2^(x+3)−2.
What is a shift to the left by 3 units and a shift down by 2 units?
For s(x) = √e^2x − 1, find functions f and g so s = g ◦ f .
What are is f(x) = e^2x − 1 and g(x) = √x