Solve by Element List Regression

Reading a Coefficient off the Graph on the SAT: Desmos Walkthrough

Read the constant in an exponential like

a\cdot b^x

by graphing it and clicking the

y

-intercept, since

f(0)

always equals the coefficient out front.

This lesson uses sliders and direct evaluation in Desmos: put the unknown constant on a slider or a single expression line and let the calculator find the value instead of solving algebra by hand.

Take this lesson interactively

A real SAT-style question

For the exponential function $f$ , the value of $f left parenthesis 0 right parenthesis$ is $c$ , where $c$ is a constant. Of the following equations that define the function $f$ , which equation shows the value of $c$ as the coefficient or the base?

$f (x) = 22 {(1.5)}^{x + 1}$

$f left parenthesis x right parenthesis equals 33 left parenthesis 1.5 right parenthesis Superscript x$

$f (x) = 49.5 {(1.5)}^{x - 1}$

$f (x) = 74.25 {(1.5)}^{x - 2}$

How to solve it in Desmos, step by step

The idea

For any exponential f(x) = a times b raised to x, plugging in x = 0 gives f(0) = a, because b raised to 0 is 1. So c = f(0) always equals the coefficient out front. Graph choice B and read the y-intercept gray point to confirm c = 33 sits in the coefficient spot.

1
Step 1
Type this. Desmos draws choice B as a curve and automatically marks its y-intercept with a gray dot on the y-axis.
Type in Desmos
$y=33\left(1.5\right)^{x}$
2
Step 2
Click the gray dot where the curve crosses the y-axis. Desmos shows the point (0, 33), so f(0) = 33. That 33 is exactly the coefficient written in front, so choice B shows c as the coefficient. B is the answer.
3
Step 3
Optional check. Type this to mark the y value 33 with a horizontal line and confirm the curve crosses the y-axis right at it.
Type in Desmos
$y=33$

The answer is B.

$f left parenthesis x right parenthesis equals 33 left parenthesis 1.5 right parenthesis Superscript x$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

For the exponential function

f

, the value of

f(0)

c

, where

c

is a constant. Of the following equations that define the function

f

, which equation shows the value of

c

as the coefficient or the base?

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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