Question
The graph of f(x) = x was transformed to create the graph of g(x) = f(x) + 4. What is the graph of g?
Answers
GPT-4o mini
The graph of the function \( f(x) = x \) is a straight line that passes through the origin with a slope of 1.
When transforming \( f(x) \) into \( g(x) = f(x) + 4 \), you're adding 4 to the output of the function \( f(x) \). This transformation results in a vertical shift of the graph.
Specifically, for every point \( (x, f(x)) \) on the graph of \( f(x) \), the corresponding point on the graph of \( g(x) \) will be \( (x, f(x) + 4) \).
Thus, the graph of \( g(x) = f(x) + 4 \) is the graph of \( f(x) = x \) shifted upwards by 4 units. This means that the new line will pass through the point (0, 4) instead of the origin, and will still have a slope of 1.
In summary, the graph of \( g(x) = f(x) + 4 \) is a straight line with a slope of 1 that intersects the y-axis at (0, 4).
When transforming \( f(x) \) into \( g(x) = f(x) + 4 \), you're adding 4 to the output of the function \( f(x) \). This transformation results in a vertical shift of the graph.
Specifically, for every point \( (x, f(x)) \) on the graph of \( f(x) \), the corresponding point on the graph of \( g(x) \) will be \( (x, f(x) + 4) \).
Thus, the graph of \( g(x) = f(x) + 4 \) is the graph of \( f(x) = x \) shifted upwards by 4 units. This means that the new line will pass through the point (0, 4) instead of the origin, and will still have a slope of 1.
In summary, the graph of \( g(x) = f(x) + 4 \) is a straight line with a slope of 1 that intersects the y-axis at (0, 4).