What is the transformation rule for the function $$y=x^2$$ when transformed by $$T(x,y)\rightarrow(x+4,y-8)$$ ?

The transformed function is $$y+8=(x-4)^2$$ .

Factor the polynomial $$x^3 + x^2 + 9x - 9$$ .

The factored form is $$(x+3)(x-3)(x-1)$$ .

Find the composition of functions $$f(x)=\sqrt{5-2x}$$ and $$g(x)=x^2-4$$ , denoted as $$(f \circ g)(x)$$ .

The result is $$\sqrt{-2x^2 + 13}$$ .

What is the axis of symmetry for the parabola $$y = 2(x-3)^2 + 4$$ ?

The axis of symmetry is the line $$x = 3$$ .

What is the quadratic formula used to find the roots of a quadratic equation?

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What does it mean for a function to be even?

A function is even if $$f(-x) = f(x)$$ for all x in the domain.

What does it mean for a function to be odd?

A function is odd if $$f(-x) = -f(x)$$ for all x in the domain.

What is the difference between a polynomial and a rational function?

A polynomial is a function of the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , while a rational function is the ratio of two polynomials.

What is the significance of the discriminant in a quadratic equation?

The discriminant $$D = b^2 - 4ac$$ determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D

How do you find the y-intercept of a function?

The y-intercept is found by evaluating the function at $$x = 0$$ .

What is the relationship between the roots and the coefficients of a polynomial?

For a polynomial of the form $$a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , the sum and product of the roots can be related to the coefficients using Vieta's formulas.

Pre-Calculus Review

Flashcard

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Mathematics

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11th Grade

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Practice Problem

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Easy

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CCSS

HSA.APR.B.2, HSA-REI.B.4B, HSF.BF.B.3

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The degree is 6.

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