What you’ll learn
Compare functions represented by graph/table/equation.
Key idea
Starting height, output at a specified input and rate of change are different properties.
Starting value and slope are separate; comparison requires both evaluated values at the same input.
Worked example
Enter the exact value or ordered values in the format requested below.
Full straight f graph joins F marks; x horizontal, y vertical. h(x)=1x+2. Compare at x=2. Enter h>f, f>h or h=f AND both outputs, e.g. h>f;f(2)=...;h(2)=....
Marked coordinates: F=(2, 3); F=(1, 1); F=(0, -1).
- Read f(2)=3 and evaluate h(2)=1(2)+2=4; comparison h>f.
- f rises 2 per input unit while h rises 1; f starts lower (-1<2) but its slope is greater. Plotted values and slopes are separate comparisons.
Answer: h>f;f(2)=3;h(2)=4
Quick Check
Relate the graph used in 'Compare functions represented by graph/table/equation' to an equation, table, transformation, or verbal description.
Full straight f graph joins F marks. h(x)=1x+9. Claim: "f grows more slowly because its initial output 2 is below h initial 9." Assess using graph and equation rates.
Marked coordinates: F=(2, 6); F=(1, 4); F=(0, 2).