Question

Graph the given functions on a common screen. How are these graphs related?

y= 3*, y = 10*, y=(), (10) y= The functions with bases greater than 1 (3 and 10*) are Select-- while those with bases less than 1 [() and (1) a 3* about the ?-axis, and the graph of faster as?. are Select-- The graph of ()* is the reflection of that of is the reflection of that of 10 about the ?-axis. The graph of 10 increases more quickly than that of 3* for x? 0, and approaches

Answer 1

To graph the given functions, we need to understand their properties. The linear functions have a straight line graph, while the quadratic and square root functions have curved graphs. The linear function with a larger slope (10x) increases more quickly than the one with a smaller slope (3x). The quadratic function has a parabolic shape, while the square root function has an increasing but decreasing slope.

Step-by-step explanation:

To graph the given functions, we need to understand their properties. The first function, y = 3x, represents a linear equation with a slope of 3. The second function, y = 10x, also represents a linear equation but with a steeper slope of 10. The third function, y = x^2, represents a quadratic equation with a parabolic shape. The fourth function, y = √x, represents a square root function with a decreasing slope as x increases.

The graph of y = 3x will be a straight line that starts at the origin (0,0) and goes up at a 45-degree angle. The graph of y = 10x will have the same starting point but will go up at a steeper angle. The graph of y = x^2 will have a U-shaped curve, while the graph of y = √x will start at the origin and curve to the right.

So, the graphs of these functions are related by their shapes and slopes. The linear functions have a straight line graph, while the quadratic and square root functions have curved graphs. The linear function with a larger slope (10x) increases more quickly than the one with a smaller slope (3x). The quadratic function has a parabolic shape, while the square root function has an increasing but decreasing slope.