Question

Suppose f(x) = x³ . find the graph of f(x) -5

Answer 1

Graph 4 is the correct graph of f(x) - 5.

To find the graph of f(x) - 5, we can start by graphing the graph of f(x) and then shifting it down by 5 units.

The graph of f(x) is a cubic function, which means that it is a graph of the form y = ax³ + bx² + cx + d. To graph a cubic function, we can use the following steps:

Find the x-intercepts of the graph. The x-intercepts are the points where the graph crosses the x-axis. To find the x-intercepts, we set y = 0 and solve the equation for x.

Find the y-intercept of the graph. The y-intercept is the point where the graph crosses the y-axis. To find the y-intercept, we set x = 0 and solve the equation for y.

Find the end behavior of the graph. As x approaches positive or negative infinity, what does the value of y approach?

Plot the x-intercepts, y-intercept, and any other important points on the graph.

Connect the points with a smooth curve.

To graph the graph of f(x) - 5, we simply shift the graph of f(x) down by 5 units.

The description matches graph 4.

Answer 2

Choice 4

Explanation:

The parent function is
`y=x^3.` The graph of the function

• 
  `y=x^3+a` is translated a units up graph of the parent function;
• 
  `y=x^3 -a` is translated a units down graph of the parent function;
• 
  `y=(x-a)^3` is translated a units to the right graph of the parent function;
• 
  `y=(x+a)^3` is translated a units to the left graph of the parent function.

In your case, the graph of the function
`f(x)=x^3-5` is translated 5 units down graph of the function
`y=x^3.` This is choice 4