Question

Write the functions by the graphs
F(x)=
G(x)=
H(x)=

Answer 1

f(x) = |x|

g(x) = |x| - 2

h(x) = |x| + 3

Explanation:

All the functions graphed represent the absolute value functions.

Since function g(x) passes through (0, 0) and (1, 1),

Let the equation of a line passing through these points is,

y = mx + b

Slope of the line passing through these points 'm' =
`\frac{\text{Rise}}{\text{Run}}=(1-0)/(1-0)`

m = 1

y-intercept of the line 'b' = 0

Therefore, equation of the line will be,

y = x

And the function representing the two lines (both are the mirror images) joining at the origin will be,

f(x) = |x|

When the parent function is shifted 3 units up, the new function will be

h(x) = |x| + 3

When the parent function is shifted 2 units down,

g(x) = |x| - 2