11th Grade Mathematics Quiz CJ

Evaluate the step function $f(x) = \lceil x \rceil$ at $x = -2.3$.

• -3

• -2

• -2.3

• -1

Evaluate the step function $f(x) = \lfloor x \rfloor$ at $x = 3.7$.

• 3

• 4

• 3.7

• 2

Multiply the binomials $(x + 3)(x - 4)$.

• $x^2 - x - 12$

• $x^2 + 7x + 12$

• $x^2 - 7x - 12$

• $x^2 - x + 12$

Transform the quadratic function $f(x) = x^2$ by stretching it vertically by a factor of 2 and shifting it 1 unit to the left. What is the new function?

• $f(x) = 2(x + 1)^2$

• $f(x) = 2(x - 1)^2$

• $f(x) = (2x + 1)^2$

• $f(x) = (2x - 1)^2$

Subtract the polynomial $2x^2 + x - 1$ from $4x^2 - 3x + 2$.

• $2x^2 - 4x + 3$

• $2x^2 - 2x + 1$

• $2x^2 - 4x + 1$

• $2x^2 + 4x + 3$

Evaluate the step function $f(x) = \lfloor x \rfloor$ at $x = -0.5$.

• -1

• 0

• -0.5

• 1

Subtract the polynomial $3x^2 - 4x + 5$ from $5x^2 + 2x - 3$.

• $2x^2 + 6x - 8$

• $8x^2 - 6x + 8$

• $2x^2 + 6x - 8$

• $2x^2 + 6x - 2$

Transform the quadratic function $f(x) = x^2$ by reflecting it over the x-axis and shifting it 4 units down. What is the new function?

• $f(x) = -x^2 + 4$

• $f(x) = -x^2 - 4$

• $f(x) = x^2 - 4$

• $f(x) = x^2 + 4$

Find the roots of the polynomial $x^2 + 4x + 4$.

• $x = -2, x = -2$

• $x = 2, x = -2$

• $x = -4, x = 0$

• $x = 0, x = 4$

Transform the quadratic function $f(x) = x^2$ by shifting it 3 units up and 2 units to the right. What is the new function?

• $f(x) = (x - 2)^2 + 3$

• $f(x) = (x + 2)^2 + 3$

• $f(x) = (x - 2)^2 - 3$

• $f(x) = (x + 2)^2 - 3$