Graph the following functions to find the solution(s) to f, of, x, equals, g, of, xf(x)=g(x).
f, of, x, equals, left parenthesis, x, plus, 2, right parenthesis, cubed, minus, 4f(x)=(x+2) 
3
 −4
g, of, x, equals, minus, start fraction, 3, divided by, 4, end fraction, x, minus, start fraction, 15, divided by, 4, end fractiong(x)=− 
4
3
​
 x− 
4
15
​
 
Answer
Attempt 1 out of 2

The graph above shows the functions \( f(x) = (x + 2)^3 - 4 \) and \( g(x) = -\frac{3}{4}x - \frac{15}{4} \). The solutions to \( f(x) = g(x) \) correspond to the points where the two curves intersect.

From the graph, you can visually estimate these points of intersection, which represent the solution(s) to the equation \( f(x) = g(x) \).

Would you like a more detailed analysis of the intersection points, or do you have any questions?

Here are five related questions:
1. How do you algebraically solve \( f(x) = g(x) \) for the intersection point(s)?
2. Can you confirm the intersection points by substituting values back into the equations?
3. How do transformations of cubic functions affect their graphs?
4. What is the significance of the slope and intercept in the linear function \( g(x) \)?
5. How would the graph change if we modified the coefficients of \( f(x) \) or \( g(x) \)?

**Tip**: When graphing functions, always check for key features such as intercepts and symmetry to guide your understanding of the behavior.

Graph the following functions to find the solution(s) to f(x) = g(x). f(x) = (x + 2)^3 − 4 and g(x) = −(3/4)x − (15/4).

Learn how to graph the cubic function f(x) = (x + 2)^3 − 4 and the linear function g(x) = −(3/4)x − (15/4) to find their points of intersection. This tutorial covers key concepts in graphing functions, solving equations, and analyzing intersections. Suitable for students in Grades 10-12.

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