Math Problem Statement

Use the graph of each function to estimate the indicated function values. Then confirm the estimate algebraically. Round to the nearest hundredth, if necessary.

Solution

The image presents four graphs, each with corresponding function estimates to solve. Let's go through them step by step:

  1. Graph 1: g(x)=5x+50g(x) = -5\sqrt{x} + 50

    • Estimate g(6),g(12),g(19)g(6), g(12), g(19) using the graph.
  2. Graph 2: g(x)=x38x2+8xg(x) = x^3 - 8x^2 + 8x

    • Estimate g(2),g(1),g(8)g(-2), g(1), g(8) from the graph.
  3. Graph 3: f(x)=x+2f(x) = |x| + 2

    • Estimate f(8),f(3),f(0)f(-8), f(-3), f(0) from the graph.
  4. Graph 4: Piecewise function P(x)P(x)

    • Estimate P(6),P(2),P(9)P(-6), P(2), P(9).

I'll guide you through solving each one. Let's start with Graph 1, where we'll estimate the values directly from the graph. Would you like detailed assistance with each part?

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Math Problem Analysis

Mathematical Concepts

Graph interpretation
Function estimation
Absolute value functions
Piecewise functions
Polynomials

Formulas

Square root function: g(x) = -5√x + 50
Cubic polynomial: g(x) = x^3 - 8x^2 + 8x
Absolute value function: f(x) = |x| + 2
Piecewise function: P(x) = {-3 if x < 2; 1 - 1/x if x ≥ 2}

Theorems

Graphical estimation
Piecewise function evaluation

Suitable Grade Level

Grades 9-12