Honors Non-Linear Functions and Equations

Domain and Range

100

h(x)=20/x

a. find h(4)

b. find h(-5)

c.  find h(x)=10

a. h(4) = 5

b. h(-5) = -4

c. h(2)=10.....so x = 2

200

What is the theoretical domain and range of 

y=5/x

Domain:  

x!=0

Range: 

y!=0

300

A function 

I(d)=8/d^2

 Find the values of d that will satisfy the following equations. 

 a. I(d)=8 

 b. I(d)=-5 

 c. I(d)=0 

What is 

 a. 

d=+-1

b. No solution

c. No solution

400

Find the theoretical domain and range of the function

 s(t)=-16t² -48t+160

Domain: t = all real numbers

Range: 

s(t)<=196

500

Steve is throwing a ball off of a building with an initial height of 160 feet and initial upward velocity of 48 feet per second.  Given the equation 

s(x)=-16x^2+48x+160

, find the practical domain and range of the function. 

Domain: 0 ≤ x ≤5  

Range: 0 ≤ s(x) ≤ 196

Factor (NO CALC)

100

NO CALC

Factor 3x²+17x+20

(3x +5)(x+4)

200

NO CALC

Factor 

16x^2-6x-1

(8x+1)(2x-1)

300

NO CALC

Factor 

4x^2+40x+100

4(x+5)²

400

Factor 12x² - 75

NO CALC

3(2x-5)(2x+5)

500

Factor 14x² + 77x - 42

NO CALC

7(2x-1)(x+6)

Solve (NO CALC)

100

How many solutions can you have when solving a quadratic equation? 

What are 2, 1, or 0 (no real solutions)

200

Solve   3x-2=x²+11x+14

NO CALC

What is x=-4

300

Solve 2x=2x²-4x

NO CALC

What x=0 or 3

400

Solve the following equation for the intersection point(s) by using algebra 

 -3-x=x²+3x+1

NO CALC

What x = -2

500

Solve 4x²+13x=5x+9

NO CALC

What is 

-1 +-sqrt13/2 or (-2+-sqrt13)/2

Quadratics (NO CALC)

100

Identify the y intercept, x intercept(s), and the vertex (max or min point) for  y=(x+3)(x-1)

NO CALC

What is x intercepts (-3,0) (1,0) y intercept -3 and vertex (-1, -4) for   y= x²-2x-3

200

Graph the y intercept, x intercept(s), and the vertex (max or min point) -2(x+2)(x-3)

NO CALC

What is x-intercepts (-2,0) and (3, 0), y-intercept 12, and maximum 

(1/2, 25/2)

 for y=2x²+2x+12

300

Write the following in standard form with the given information x-intercepts at (-2,0) and (6, 0) with y-intercept at (0, -60)

NO CALC

What is 

y=5x^2-4x-60

400

Write the following in standard form with the given information x-intercepts at (2,0) and (6, 0) with Maximum point at (4, 2)

NO CALC

What is 

y=-1/2 x^2 +4x-6

500

Write the following in standard form with the given information x-intercepts at (0,0) and (6, 0) with the graph opening upward

NO CALC

What is 

y=ax^2-6ax

 when a > 0 

Miscellaneous (NO CALC)

100

Write the following expression in standard form (2x+7)(2x-7)

NO CALC

What is 4x²+28x-49

200

Factor the following quadratic expression 5x²+35x+50

NO CALC

What is 5(x+5)(x+2)

300

Solve   x²-9x+20=20

NO CALC

What is x=0 and x=9

400

Put the following in standard form 3(x+20)(x+1)

NO CALC

What is 3x²+63x+60

500

Solve the quadratic expression for the x-intercepts by factoring or using the quadratic formula. 6x²+7x-10=-5

NO CALC

What is (-5/3, 0) (1/2, 0)