Transformaciones de la función exponencial

What is the general form of an exponential function?

• y = a * x^b

• y = a * b^x

• y = a + b^x

• y = a * b * x

How does the value of 'a' in the function y = a^x affect the graph?

• It shifts the graph horizontally

• It changes the color of the graph

• It has no effect on the graph

• It stretches or compresses the graph vertically.

Explain how the function y = 2^x differs from the function y = 3^x in terms of transformations.

• They have the same slope

• They have the same y-intercept

• They have the same exponential growth rate

• They have different base values

What is the effect of a negative value of 'a' in the function y = a^x?

• The function will have no effect on the output

• The function will alternate between positive and negative values as x changes.

• The function will always be positive

• The function will become a straight line

If the function y = 2^x is stretched vertically by a factor of 3, what is the new function?

• y = 3 * 2^x

• y = 2^3x

• y = 3^2x

• y = 2^(3x)

Explain how the function y = 2^(x-2) differs from the function y = 2^x in terms of transformations.

• Vertical stretch by a factor of 2

• Horizontal translation of 2 units to the right

• Vertical translation of 2 units up

• Horizontal translation of 2 units to the left

If the function y = 2^x is compressed horizontally by a factor of 2, what is the new function?

• y = 2^(x/2)

• y = 2^(x-2)

• y = 2^(2x)

• y = 2^(x+2)

What is the effect of adding a constant 'c' to the exponent in the function y = 2^(x+c)?

• Shifts the graph horizontally

• Reflects the graph over the x-axis

• Changes the slope of the graph

• Shifts the graph vertically