Question

1. catalina graphed the linear parent function $f(x) = x$ and $g(x) = f(x) + 1$ on the same coordinate grid. which statement describes how the graphs of f and g are related?

the graph of the function $f(x)$ is shifted up 1 unit to produce $g(x)$.
the graph of the function $f(x)$ is shifted down 1 unit to produce $g(x)$.
the graph of the function $f(x)$ is shifted right 1 unit to produce $g(x)$.
the graph of the function $f(x)$ is shifted left 1 unit to produce $g(x)$.

Explanation:

Para funciones lineales, la transformación \( g(x)=f(x)+k \) implica un desplazamiento vertical. Si \( k > 0 \), el gráfico de \( f(x) \) se desplaza hacia arriba \( k \) unidades. Aquí, \( g(x)=f(x)+1 \), donde \( k = 1>0 \), por lo que el gráfico de \( f(x) \) se desplaza hacia arriba 1 unidad para obtener \( g(x) \).

Answer:

The graph of the function \( f(x) \) is shifted up 1 unit to produce \( g(x) \).