The function f is defined as f(x)=3x-2. What is the x-coordinate of the point on the function's graph that is closest to the origin?

Question

The function  f is defined as  f(x)=3x-2. What is the  x-coordinate of the point on the function's graph that is closest to the origin?

Bytelearn · Accepted Answer

Define Distance Formula: To find the point on the graph of the function f(x) = 3x - 2 that is closest to the origin, we need to minimize the distance from any point (x, f(x)) on the graph to the origin (0,0). The distance D between the point (x, f(x)) and the origin (0,0) can be found using the distance formula: D = √((x - 0)² + (f(x) - 0)²).Substitute f(x): Substitute f(x) with 3x - 2 into the distance formula: D = √(x² + (3x - 2)²).Expand Expression: Expand the expression inside the square root: D = √(x² + (9x² - 12x + 4)).Combine Like Terms: Combine like terms inside the square root: D = √(10x² - 12x + 4).Minimize Expression: To find the minimum distance, we can minimize the expression inside the square root since the square root function is increasing. This is equivalent to minimizing the quadratic expression 10x² - 12x + 4. To find the minimum of a quadratic function, we can use the vertex formula x = -b/(2a), where the quadratic is in the form ax² + bx + c.Apply Vertex Formula: Apply the vertex formula to the quadratic expression 10x² - 12x + 4. Here, a = 10 and b = -12. So, x = -(-12)/(2*10) = 12/20 = 0.6.Find x-coordinate: The x-coordinate of the point on the graph of the function that is closest to the origin is 0.6. This is the final answer.

The function $f$ is defined as $f(x)=3 x-2$ . $\newline$ What is the $x$ -coordinate of the point on the function's graph that is closest to the origin?

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The function f f f is defined as f(x)=3x−2 f(x)=3 x-2 f(x)=3x−2.\newlineWhat is the x x x-coordinate of the point on the function's graph that is closest to the origin?

The function $f$ is defined as $f(x)=3 x-2$ . $\newline$ What is the $x$ -coordinate of the point on the function's graph that is closest to the origin?