Question

What is the equation of the function shown in the graph, given the equation of the parent function is f(x)=3.5x ? Responses g(x)=3.5x−2 g begin argument x end argument equals 3.5 begin power x end power minus 2 g(x)=3.5x+1 g begin argument x end argument equals 3.5 begin power x end power plus 1 g(x)=3.5x−1 g begin argument x end argument equals 3.5 begin power x end power minus 1 g(x)=3.5x+1.5

Answer 1

The equation of the function shown in the graph, given the equation of the parent function is f(x) = 3.5x, is g(x) = 3.5x - 1.

To find the equation of the function, we need to analyze the graph and see how it differs from the parent function.

From the graph, we can see that the function starts infinitely close in the third quadrant and increases towards a dashed horizontal line at y = -2. It also passes through the point (0, -1) and continues to increase through the point (1, -1.5) in the first quadrant.

Based on this information, we can determine that the function has been shifted downward by 1 unit and the slope remains the same.

Therefore, the equation of the function is g(x) = 3.5x - 1.

This equation represents a linear function with a slope of 3.5 and a y-intercept of -1.