Math Problem Statement

Установите соответствие между видом функции и её названием: 1) y = x^n; 2) y = a^x; 3) y = -k/x; 4) y = kx + b.

Solution

To match the types of functions in the table with their corresponding names:

Вид функцииНазвание
y=xny = x^nБ: степенная
y=axy = a^xВ: показательная
y=kxy = -\frac{k}{x}Г: обратная пропорциональность
y=kx+by = kx + bА: линейная

Explanation:

  1. y=xny = x^n: This is a power function (степенная функция) where nn is the power of xx. Hence, it matches Б.
  2. y=axy = a^x: This is an exponential function (показательная функция), where a>0a > 0 and a1a \neq 1. Hence, it matches В.
  3. y=kxy = -\frac{k}{x}: This is an inverse proportionality (обратная пропорциональность) because xx appears in the denominator. Hence, it matches Г.
  4. y=kx+by = kx + b: This is a linear function (линейная функция) because it follows the form y=mx+cy = mx + c. Hence, it matches А.

Final Matching:

1 → Б
2 → В
3 → Г
4 → А

Let me know if you need further clarification!


Related Questions:

  1. What are the general forms of power and exponential functions?
  2. How do linear and inverse proportional functions differ visually?
  3. What are real-life applications of exponential functions?
  4. How do you graph the function y=kxy = -\frac{k}{x}?
  5. What is the difference between exponential growth and linear growth?

Tip:

To identify a function type, look at the position of xx: in power functions, xx is the base; in exponential functions, xx is the exponent.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions and Graphs

Formulas

Power function: y = x^n
Exponential function: y = a^x
Inverse proportionality: y = -k/x
Linear function: y = kx + b

Theorems

-

Suitable Grade Level

Grades 9-11