Math Problem Statement

  1. Gambarlah grafik fungsi-fungsi dibawah ini : a. 𝑦 = 3𝑥 + 3 b. 𝑦 = −3𝑥 + 3 c. 𝑦 = 2𝑥2 d. 𝑦 = 𝑥3 + 1 Tentukan D(f) dan R(f)

Solution

Here are the graphs of the functions you requested, along with their domains and ranges:

  • y = 3x + 3:

    • Domain (D(f)): R\mathbb{R} (all real numbers)
    • Range (R(f)): R\mathbb{R} (all real numbers)
  • y = -3x + 3:

    • Domain (D(f)): R\mathbb{R} (all real numbers)
    • Range (R(f)): R\mathbb{R} (all real numbers)
  • y = 2x^2:

    • Domain (D(f)): R\mathbb{R} (all real numbers)
    • Range (R(f)): [0,)[0, \infty)
  • y = x^3 + 1:

    • Domain (D(f)): R\mathbb{R} (all real numbers)
    • Range (R(f)): R\mathbb{R} (all real numbers)

Do you have any questions or need further clarification?

Here are 5 related questions to explore:

  1. What is the effect of changing the slope in linear functions like y=3x+3y = 3x + 3?
  2. How would the graph of y=2x2y = 2x^2 change if we modify the coefficient of x2x^2?
  3. What is the significance of the y-intercept in linear functions?
  4. How does the graph of y=x3+1y = x^3 + 1 compare to y=x3y = x^3?
  5. What would the graph of y=2x2y = -2x^2 look like?

Tip: The domain of a polynomial function is always R\mathbb{R} (all real numbers), unless stated otherwise.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Quadratic Functions
Cubic Functions
Domain and Range

Formulas

y = mx + c (Linear function)
y = ax^2 + bx + c (Quadratic function)
y = x^3 + c (Cubic function)

Theorems

Domain and Range Theorem
Basic Properties of Polynomial Functions

Suitable Grade Level

Grades 9-12