Question

Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x)−7 ?

The graph of g(x) is the graph of​​​ f(x) translated 7 units down.

The graph of g(x) is the graph of​ f(x)​ vertically stretched by a factor of 7.

The graph of g(x) is the graph of​​ f(x)​ vertically compressed by a factor of 7.

The graph of g(x) is the graph of f(x) translated 7 units left.

Answer 1

The graph of g(x) is the graph of f(x) translated 7 units down, which retains the original slope but lowers the entire graph by 7 units on the y-axis.

Step-by-step explanation:

The question asks about the relationship between the graphs of two functions, f(x)=x and g(x)=f(x)−7. The graph of f(x)=x is a straight line with a slope of 1 because it represents a direct relationship between x and y with the y-intercept being at the origin (0,0). When we subtract 7 from f(x), the result is the function g(x)=x−7, which translates the original graph 7 units down along the vertical axis. It is important to note the difference between translations and transformations like stretches or compressions. Only the y-values have changed by a constant amount, and since there is no change in the slope of the line, there is no vertical stretching or compression.