Intersections as Solutions
Aligned to A-REI.D.11 — Common Core State Standards for Mathematics.
What this lesson teaches
Where the graphs of y = f(x) and y = g(x) cross, the two functions share the same x and y values. That shared x-coordinate is exactly a value that makes f(x) = g(x), so intersection points are solutions of the equation.
Worked example
Solve f(x) = g(x) where f(x) = x + 1 and g(x) = 2x − 3. Set them equal: x + 1 = 2x − 3. Subtract x: 1 = x − 3, so x = 4. Then y = 4 + 1 = 5, meaning the graphs intersect at the point (4, 5).
Practice questions
- Find where y = 3x and y = x + 4 intersect.
- Solve x^2 = x + 2 by setting the functions equal.
- Explain why an intersection point gives a solution to f(x) = g(x).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Intersecciones como Soluciones
Donde las gráficas de y = f(x) y y = g(x) se cruzan, ambas funciones comparten el mismo valor de x y de y. Esa coordenada x compartida es exactamente un valor que hace f(x) = g(x), por lo que los puntos de intersección son soluciones de la ecuación.
Ejemplo: Resuelve f(x) = g(x) donde f(x) = x + 1 y g(x) = 2x − 3. Iguálalas: x + 1 = 2x − 3. Resta x: 1 = x − 3, así que x = 4. Luego y = 4 + 1 = 5, es decir, las gráficas se cruzan en el punto (4, 5).
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