Simplify the expression using the properties of exponents. Show all your work. (3 points)
Simplify the expression using the properties of exponents. Show all your work. (3 points)
Simplify the expression using the properties of exponents. Show all your work. (3 points)
Tell whether the function is an example of exponential growth or exponential decay. Briefly explain how you know. (2 points)
Tell whether the function is an example of exponential growth or exponential decay. Briefly explain how you know. (2 points)
Write a new exponential function with base e as f(x) = ex that represents the indicated transformations. (3 points)
“a translation one unit to the left, reflection across the x-axis, and down three units”
Write a new exponential function with base e as f(x) = ex that represents the indicated transformations. (3 points)
“a translation four units right; vertical shrink by a factor of 1/3, and a translation six units up”
Describe the transformations for the function. (3 points)
Describe the transformations for the function. (3 points)
Describe the graph of the function and complete the table of values for the transformations. Graph the function. Identity the horizontal asymptote, domain, and range. (10 points total)
Describe the graph of the function and complete the table of values for the transformations. Graph the function. Identity the horizontal asymptote, domain, and range. (10 points total)
Rewrite the logarithmic equation into an exponential equation. (1 point)
Rewrite the logarithmic equation into an exponential equation. (1 point)
Rewrite the exponential equation into a logarithmic equation. (1 point)
Rewrite the exponential equation into a logarithmic equation. (1 point)
Evaluate the logarithm without using a calculator. (2 points)
Evaluate the logarithm without using a calculator. (2 points)
Evaluate the logarithm without using a calculator. (2 points)
Write a new logarithmic function from the parent function f(x) = log2x that represents the indicated transformations. (3 points)
“a translation 4 units right; reflection across the x-axis; and a translation down 5 units”
Write a new logarithmic function from the parent function f(x) = log2x that represents the indicated transformations. (3 points)
“a translation 1 unit left, a translation 4 units up, and a vertical stretch by a factor of 7/6”
Describe the transformations for the logarithmic function. (3 points)
Describe the transformations for the logarithmic function. (3 points)
Describe the graph of the function based on its transformations. Graph the function by first rewriting the parent function in exponential form to find four good coordinates. Then take the inverse of those coordinates to find the coordinates of the logarithmic parent function. Finally complete the transformations on the coordinates of the logarithmic parent function. Identity the vertical asymptote, domain, and range. (10 points total)
Describe the graph of the function based on its transformations. Graph the function by first rewriting the parent function in exponential form to find four good coordinates. Then take the inverse of those coordinates to find the coordinates of the logarithmic parent function. Finally complete the transformations on the coordinates of the logarithmic parent function. Identity the vertical asymptote, domain, and range. (10 points total)