Question

in the xy-plane, what is the y-coordinate of the y-intercept of the function f defined by f(x) = 3x⁴ - 4x³ + 55?

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is the value of \(y\) when \(x = 0\). So we need to substitute \(x=0\) into the function \(f(x)=3x^{4}-4x^{3}+55\).

Step2: Substitute \(x = 0\) into the function

When \(x = 0\), we have \(f(0)=3(0)^{4}-4(0)^{3}+55\). Since any non - zero number to the power of \(0\) is \(1\), but \(0\) to any positive power is \(0\). So \(3(0)^{4}=3\times0 = 0\), \( - 4(0)^{3}=-4\times0 = 0\). Then \(f(0)=0 - 0+55=55\).

Answer:

The y - coordinate of the y - intercept of the function \(f(x)\) is \(55\).