Benjamin Achtenberg

Questions

• How do you describe the end behavior for #f(x)=x^5-4x^3+x+1#?
• How do you use synthetic division to divide #(5x^3-6x^2+8)div(x-4)#?
• How do you sketch the general shape of #f(x)=-x^3-4x^2+3# using end behavior?
• How do you use synthetic division to show that x=1/2 is a zero of #2x^3-15x^2+27x-10=0#?
• How do you write a polynomial with roots of –1, –2, and 3?
• What are the rational zeros for #x^3-3x^2-4x+12#?
• How do you determine the intervals for which the function is increasing or decreasing given #f(x)=1/(x+1)-4#?
• How do you find the degree and leading coefficient of the polynomial #14y+30+y^2#?
• How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=-x^3-4x#?
• How do you use the rational root theorem to find the roots of #5x^4 + 9x^3 + 5x^2 + 2x + 4 = 0#?
• How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=x^5-1#?
• How do you find all the zeros of #f(x)=x^4-x^3-3x^2-x+1#?
• How do you find the discriminant of #x^7-3x^5+x^4-4x^2+4x+4# and what does it tell us?
• How do you use the rational root theorem to find the roots of #3x^3 - kx^2 - 16x + 12 = 0#?
• How do you find the zeros of a function #f(x)= 2x^3 - 3x^2- 12x +20#?
• How do you use the rational root theorem to find the roots of #8x^3-3x^2+5x+15#?
• How do you write two functions for which #(f*g)(x)=2x^2+11x-6#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=2x+5# and #g(x)=3+x#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=x^2-9# and #g(x)=x+4#?
• What are all the possible rational zeros for #f(x)=x^6-64#?
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