Question

v. functions and models

1. the graphs of f and g are given.

a) state the values of f(-4) and g(3)
b) for what values of x if f(x) = g(x)?
c) estimate the solution of the equation f(x) = 1.
d) on what interval is f decreasing?
e) state the domain and range for f.
f) state the domain and range for g.

1. if f(x) = 3x² - x + 2, find f(2), f(a), f(-a), f(a + 1), 2f(a), f(a²), f(a)².
2. find the domain of each function.

a) f(x) = \\(\frac{x}{3x - 1}\\) b) g(u) = \\(\sqrt{u} + \sqrt{4 - u}\\)

1. find the expression for the bottom half of the parabola x + (y - 1)² = 0.
2. find the expression for the function whose graph is the given curve. (hint: piece - wise function)
3. match each equation with its graph. explain your choices. (don’t use a computer or graphing calculator).

a) y = x² b) y = x⁵ c) y = x⁸

Explanation:

Step1: 确定f(-4)的值

观察函数f的图像，找到x = -4对应的y值。从图中可以看出，当x = -4时，f(-4) = 2。

Step2: 确定g(3)的值

观察函数g的图像，找到x = 3对应的y值。从图中可以看出，当x = 3时，g(3) = 2。

Answer:

f(-4) = 2，g(3) = 2。

（注：以上是针对70题a小问的解答，若需要解答其他小问或其他题目，请提供具体问题。）