Writing Exponential Functions from Graphs

The video tutorial explains how to write exponential functions from graphs. It covers the identification of key components such as the y-intercept and the common ratio, which are essential for forming the equation of an exponential function. The tutorial provides step-by-step examples, demonstrating how to extract these values from graphs and use them to write exponential equations. It also addresses common challenges, such as dealing with non-integer points and simplifying equations.

What is the general form of an exponential function?

• y = a + bx

• y = a * b^x

• y = ax / b

• y = a - b^x

What does 'a' represent in the exponential function equation?

• The common ratio

• The y-intercept

• The slope of the graph

• The x-intercept

How do you find the common ratio 'b' in an exponential function from a graph?

• Divide y2 by y1 using any two points

• Add y2 to y1 using any two points

• Divide y2 by y1 using two consecutive points

• Multiply y2 by y1 using two consecutive points

Why might it be useful to create a table when determining the common ratio from a graph?

• To draw the graph more accurately

• To calculate the x-intercept

• To organize the y-values clearly

• To organize the x-values clearly

What is the equation of an exponential function if the y-intercept is 3 and the common ratio is 2?

• y = 2 * 3^x

• y = 3 + 2x

• y = 3 * 2^x

• y = 3 / 2^x

If the y-intercept is 4 and the common ratio is 0.5, what is the exponential function equation?

• y = 4 * 0.5^x

• y = 4 / 0.5^x

• y = 0.5 * 4^x

• y = 4 + 0.5x

What does a common ratio greater than 1 indicate about the exponential function?

• It is decreasing

• It is increasing

• It is constant

• It is oscillating

In an exponential function, if the y-intercept is 1 and the common ratio is 3, what is the correct equation?

• y = 1 / 3^x

• y = 1 + 3x

• y = 3 * 1^x

• y = 1 * 3^x

How does the value of 'b' affect the shape of the exponential function's graph?

• It determines the symmetry of the graph

• It determines the y-intercept

• It determines the x-intercept

• It determines the steepness and direction of growth

What is the equation if the y-intercept is 5 and the common ratio is 2.5?

• y = 2.5 * 5^x

• y = 5 * 2.5^x

• y = 5 / 2.5^x

• y = 5 + 2.5x