A point on a function’s graph is an input-output pair: the first coordinate goes into the rule, and the second is the result. Substitute that input, then solve for the unknown constant. In Desmos, you can use a regression with to find it. The key trap is dropping an exponent, which changes the number multiplying the constant.
Hints
- Hint 1
A point on means . The first coordinate is the input, and the second is the output. What equation does give you?
- Hint 2
Replace with , but keep the whole parenthesis inside the cube: . Dropping the cube changes the equation you need to solve.
- Hint 3
A regression asks Desmos to find an unknown constant. Type your substituted equation with in place of , leaving as the only unknown.
Step-by-step
Use the point in a Desmos regression
Step 1Turn the point into a function fact
On the graph of , the first coordinate is the input, and the second is its output. So the point means .
- Step 2
Substitute the input
Replace with in the given rule, and set the result equal to the output, : . Keep the cube on ; dropping it changes the number multiplying .
- Step 3
Find the constant
Type . The regression uses to find the constant that makes this equation true. Desmos shows under PARAMETERS, so the value of is . Choice C.