Graphing worksheet

1. Y1 at x = 2: 2

1. Put x = 2 into Y1 = x^1 (angles in degrees) to find its y value

   $\text{Y1 =}\text{x^1}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^1}$

3. Raise to a power

   $2^1$$=2$

4. Final result

   $\text{x^1}$$=2$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=2$

6. Find the zeros. Check x from −11 to 12 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −3, y ≈ −3}$

2. Y1 at x = 3: 3

1. Put x = 3 into Y1 = x^1 to find its y value

   $\text{Y1 =}\text{x^1}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^1}$

3. Raise to a power

   $3^1$$=3$

4. Final result

   $\text{x^1}$$=3$

5. So this is the value of Y1 when x = 3

   $\text{Y1(3)}$$=3$

6. Find the zeros. Check x from −7 to 11 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −5, y ≈ −5}$

3. Y1 at x = 2: 4

1. Put x = 2 into Y1 = x^2 (angles in degrees) to find its y value

   $\text{Y1 =}\text{x^2}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^2}$

3. Raise to a power

   $2^2$$=4$

4. Final result

   $\text{x^2}$$=4$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=4$

6. Find the zeros. Check x from −9 to 8 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −1.16227766, y ≈ 1.350889359; x ≈ 5.16227766, y ≈ 26.64911064}$

4. Y1 at x = 3: 81

1. Put x = 3 into Y1 = x^4 (angles in degrees) to find its y value

   $\text{Y1 =}\text{x^4}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^4}$

3. Raise to a power

   $3^4$$=81$

4. Final result

   $\text{x^4}$$=81$

5. So this is the value of Y1 when x = 3

   $\text{Y1(3)}$$=81$

6. Find the zeros. Check x from −10 to 14 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −1.459723424, y ≈ 4.540276576; x ≈ 1.663840188, y ≈ 7.663840188}$

5. Y1 at x = 2: 4

1. Put x = 2 into Y1 = x^2 (angles in degrees) to find its y value

   $\text{Y1 =}\text{x^2}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^2}$

3. Raise to a power

   $2^2$$=4$

4. Final result

   $\text{x^2}$$=4$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=4$

6. Find the zeros. Check x from −11 to 12 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −0.8284271247, y ≈ 0.686291501; x ≈ 4.828427125, y ≈ 23.3137085}$

6. Y1 at x = 2: 8

1. Put x = 2 into Y1 = x^3 (angles in degrees) to find its y value

   $\text{Y1 =}\text{x^3}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^3}$

3. Raise to a power

   $2^3$$=8$

4. Final result

   $\text{x^3}$$=8$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=8$

6. Find the zeros. Check x from −12 to 10 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −1.532088886, y ≈ −3.596266659; x ≈ −0.3472963553, y ≈ −0.041889066; x ≈ 1.879385242, y ≈ 6.638155725}$

7. Y1 at x = 2: 2

1. Put x = 2 into Y1 = x^1 to find its y value

   $\text{Y1 =}\text{x^1}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^1}$

3. Raise to a power

   $2^1$$=2$

4. Final result

   $\text{x^1}$$=2$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=2$

6. Find the zeros. Check x from −9 to 9 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −5, y ≈ −5}$

8. Y1 at x = 2: 16

1. Put x = 2 into Y1 = x^4 to find its y value

   $\text{Y1 =}\text{x^4}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^4}$

3. Raise to a power

   $2^4$$=16$

4. Final result

   $\text{x^4}$$=16$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=16$

6. Find the zeros. Check x from −9 to 11 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −1.255937548, y ≈ 2.488124904; x ≈ 1.702706371, y ≈ 8.405412742}$

9. Y1 at x = 2: 4

1. Put x = 2 into Y1 = x^2 (angles in degrees) to find its y value

   $\text{Y1 =}\text{x^2}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^2}$

3. Raise to a power

   $2^2$$=4$

4. Final result

   $\text{x^2}$$=4$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=4$

6. Find the zeros. Check x from −10 to 8 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −1.16227766, y ≈ 1.350889359; x ≈ 5.16227766, y ≈ 26.64911064}$

10. Y1 at x = 2: 16

1. Put x = 2 into Y1 = x^4 to find its y value

   $\text{Y1 =}\text{x^4}$

2. Read the expression using the order of operations: brackets, powers, × and ÷, then + and −

   $\text{x^4}$

3. Raise to a power

   $2^4$$=16$

4. Final result

   $\text{x^4}$$=16$

5. So this is the value of Y1 when x = 2

   $\text{Y1(2)}$$=16$

6. Find the zeros. Check x from −9 to 11 in 2,000 steps for places where Y1 switches between positive and negative. Then zoom in on each one. Skip any switch where the graph jumps through infinity instead of crossing 0

   $\text{x ≈ 0, y ≈ 0}$

7. Find where the graphs meet: where Y1 − Y2 is zero, found the same way. The y there is Y1's value

   $\text{x ≈ −0.7976231098, y ≈ 0.4047537804; x ≈ 1.49453018, y ≈ 4.989060361}$