Question

use the graphing calculator to graph each function and find the matching graph.

cube root
\\(f(x) = \sqrt3{x}\\)

exponential
\\(f(x) = 2^x\\)

logarithmic
\\(f(x) = \log x\\)

Explanation:

Analyze the cube root function

Using the Cube Root Transformations knowledge point
The parent cube root function is \(f(x) = \sqrt[3]{x}\).

• Domain: all real numbers \((-\infty, \infty)\).
• Key points: \((-1, -1)\), \((0, 0)\), and \((1, 1)\).
• Graph C shows this characteristic S-shape passing through the origin \((0,0)\), \((1,1)\), and \((-1,-1)\).
• Therefore, Cube Root \(f(x) = \sqrt[3]{x}\) matches Graph C.

Analyze the exponential function

Using the Exponential Function Graphing knowledge point
The exponential function is \(f(x) = 2^x\).

• Domain: all real numbers \((-\infty, \infty)\).
• Range: \(y > 0\) (horizontal asymptote at \(y = 0\)).
• Key points: \((0, 1)\), \((1, 2)\), and \((2, 4)\).
• Graph D shows a curve that grows rapidly to the right, has a horizontal asymptote at the x-axis on the left, and passes through \((0,1)\) and \((1,2)\).
• Therefore, Exponential \(f(x) = 2^x\) matches Graph D.

Analyze the logarithmic function

Using the Logarithmic Graphing knowledge point
The logarithmic function is \(f(x) = \log_2 x\).

• Domain: \(x > 0\) (vertical asymptote at \(x = 0\)).
• Key points: \((1, 0)\), \((2, 1)\), and \((4, 2)\).
• Graph B shows a curve defined only for \(x > 0\) with a vertical asymptote at the y-axis, passing through \((1,0)\), \((2,1)\), and \((4,2)\).
• Therefore, Logarithmic \(f(x) = \log_2 x\) matches Graph B.

Answer:

Question 1

• (A) Graph A
• (B) Graph B
• (C) Graph C (Correct answer)
• (D) Graph D

Question 2

• (A) Graph A
• (B) Graph B
• (C) Graph C</mcq-correct>
• (D) Graph D (Correct answer)

Question 3

<mcq-option>(A) Graph A

• (B) Graph B (Correct answer)
• (C) Graph C
• (D) Graph D