Math Problem Statement

Реши

Реши

Solution

Let's go through the problems step-by-step. I will extract and solve each one from the image. Let me start with the first few questions.


1. Для функции f(x)=10xf(x) = \frac{10}{x}:

Find which equality is true:

  • f(2)=10f(2) = 10
  • f(2)=5f(2) = 5
  • f(2)=100f(2) = 100
  • f(2)=1f(2) = 1

Solution: f(x)=10x,f(2)=102=5.f(x) = \frac{10}{x}, \quad f(2) = \frac{10}{2} = 5. The correct answer is b)f(2)=5b) f(2) = 5.


2. Выберите функцию, график которой изображен на рисунке.

Options:

  • y=x22y = x^2 - 2
  • y=(x+2)2y = (x + 2)^2
  • y=x2+2y = x^2 + 2
  • y=(x2)2y = (x - 2)^2

Looking at the parabola in the graph:

  • The vertex of the parabola is at (0,2)(0, -2), which corresponds to y=x22y = x^2 - 2.

The correct answer is a)y=x22a) y = x^2 - 2.


3. Найдите значение аргумента, при котором значение функции y=x8y = x - 8 равно 3.

Solution: y=x8,y=3.y = x - 8, \quad y = 3. Set x8=3x - 8 = 3: x=3+8=11.x = 3 + 8 = 11. The argument xx is 11.


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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Solving equations
Graph interpretation
Monotonicity

Formulas

f(x) = 10/x
y = x^2 + k
y = x - c

Theorems

Properties of even and odd functions
Roots of equations
Quadratic function analysis

Suitable Grade Level

Grades 9-11