Task Sets: Explain intersection as solution - Common Core Math - HS Algebra

1.

The graphs of $y = f(x)$ and $y = g(x)$ intersect at the point $(3, 5)$ .

What does this tell us about the equation $f(x) = g(x)$ ?

A.

$x = 5$ is a solution to $f(x) = g(x)$ , because $5$ is the
$y$ -coordinate.

B.

$x = 3$ is a solution to $f(x) = g(x)$ , because at $x = 3$ both
functions have the same output value.

C.

$(3, 5)$ is the solution to $f(x) = g(x)$ .

D.

$y = 5$ is the solution to $f(x) = g(x)$ .

2.

A student uses graphing technology and reads an intersection point as
approximately $x = 2.3$ .

The student says: "The exact solution to the equation is $x = 2.3$ ."

Is the student correct?

A.

Yes — the graph shows the exact value.

B.

No — a graphical reading gives an approximation, not an exact solution.
The exact value must be confirmed algebraically.

C.

Yes — technology graphs are always exact because they use numerical
computation.

D.

It depends on whether the student used a graphing calculator or software.

3.

To solve $3x - 2 = x^2 - 4$ graphically, a student graphs only $y = x^2 - 4$ .

What error did the student make?

A.

The student should have graphed $y = 3x - 2 - x^2 + 4$ instead.

B.

The student graphed only one curve. They need to also graph $y = 3x - 2$
and find where the two curves intersect.

C.

The student should graph $y = x^2 - 4$ and find where it crosses the
$x$ -axis to find solutions.

D.

No error — solving $x^2 - 4 = 0$ gives solutions to the original equation.

HSA.REI.D.11 Tutor Intake — Intersections as Solutions