Question

Graph the functions y = 2x, y = x^2, and 2^x on the same grid.

Answer 1

The graph of the functions y = 2x, y =
`x^2`, and
`2^x` on the same grid would display three distinct curves. The linear function y = 2x would be a straight line passing through the origin with a slope of 2. The quadratic function y =
`x^2` would form a parabola opening upwards. The exponential function y =
`2^x` would exhibit exponential growth, rising rapidly as x increases.

Step-by-step explanation:

In the first function, y = 2x, every increase in x results in a proportional doubling of y. The slope of the line is constant at 2, indicating a steady linear growth. As x increases, y increases at a steady rate, forming a straight line that passes through the origin (0,0).

For the quadratic function y =
`x^2`, the graph takes the shape of a parabola. As x varies, the corresponding y values increase, forming a symmetric curve that opens upwards. The vertex of the parabola is at the origin (0,0), and the rate of y's increase accelerates as x moves away from zero.

In the case of the exponential function y =
`2^x`, each increment in x leads to a doubling of y. The graph showcases exponential growth, rising at an accelerating rate. As x increases, the function quickly diverges, demonstrating the characteristic steep incline associated with exponential growth. The three functions, when plotted together, would provide a comprehensive visualization of linear, quadratic, and exponential behaviors on a single coordinate plane.