Quadratic graphs- features
- 2. In this presentation, you will see… Examples showing how to find: • an element of the domain that has a given image • the image of a given element in the domain
- 3. STEPS TO FIND THE IMAGE OF A GIVEN ELEMENT IN THE DOMAIN 1. Identify the 𝑥 − 𝑣𝑎𝑙𝑢𝑒 on the graph. 2. From that value, draw a vertical line to meet the curve. 3. From that point of intersection, draw a horizontal line to intersect the y-axis. 4. Read the 𝑦 − 𝑣𝑎𝑙𝑢𝑒.
- 4. EXAMPLES
- 5. EXAMPLE 1 The function 𝑓(𝑥) is represented on the graph by the parabola shown. Let us find the value of 𝑓(𝑥) when (i) 𝑥 = −2 (ii) 𝑥 = 0 (iii) 𝑥 = 1
- 6. EXAMPLE 1 SOLUTION (i) 𝑥 = −2 Step 1: Identify 𝑥 = −2 on the graph. Step 2: Draw a vertical line to meet the curve. Step 3: From that point of intersection, draw a horizontal line to intersect the y-axis. Step 4: Read the y-value. 𝑦 = 3 Therefore, 𝒇 −𝟐 = 𝟑
- 7. EXAMPLE 1 CONT’D. Do the same for the other two values. (i) 𝑥 = 0 Follow the dashed line. 𝑦 = 3 Therefore, 𝒇 𝟎 = 𝟑 (ii) 𝑥 = 1 𝑦 = 0 Therefore, 𝒇 𝟏 = 𝟎
- 8. STEPS TO FIND AN ELEMENT OF THE DOMAIN THAT HAS A GIVEN IMAGE 1. Identify the 𝑦 − 𝑣𝑎𝑙𝑢𝑒 on the graph. 2. Draw a horizontal line to meet the curve. 3. From the points of intersection, draw vertical lines to intersect the x-axis. 4. Read the 𝑥 − 𝑣𝑎𝑙𝑢𝑒𝑠. NOTE: It is possible to get two x -values.
- 9. EXAMPLE 2 The function 𝑓(𝑥) is represented on the graph by the parabola shown. Let us find the value of 𝑥 when (i) 𝑓 𝑥 = 5 (ii) 𝑓 𝑥 = −1 (iii) 𝑓 𝑥 = 0
- 10. EXAMPLE 2 SOLUTION (i) 𝑓 𝑥 = 5 Step 1: Identify the 𝑦 − 𝑣𝑎𝑙𝑢𝑒 on the graph. Step 2: Draw a horizontal line to meet the curve. Step 3: From the points of intersection, draw vertical lines to intersect the x-axis. Read the 𝑥 − 𝑣𝑎𝑙𝑢𝑒𝑠. 𝒙 = −𝟔 𝒂𝒏𝒅 𝒙 = 𝟐
- 11. EXAMPLE 2 SOLUTION (i) 𝑓 𝑥 = −1 𝒙 = −𝟒 𝒂𝒏𝒅 𝒙 = 𝟎 (ii) 𝑓 𝑥 = 0 𝒙 = −𝟒. 𝟓 𝒂𝒏𝒅 𝒙 = 𝟎. 𝟓
- 12. The End!