Question

Consider the function. f(x)=|x-4| select all the true statements. a. the x-intercept of the function is -4. b. the y-intercept of the function is 4. c. the domain of the function is x. d. the function is positive in the interval -[infinity]

Answer 1

Explanation:

See the attached graph. The questions can be answered upon reflection of what f(x)=Ix-4I looks like when graphed. The 4 statement may be evaluated using the graph.

a. the x-intercept of the function is -4. [NO - the point (-4,0) is not on the x-intercept]

b. the y-intercept of the function is 4. [YES - the point (0,4) is on the x-intercept]

c. the domain of the function is x∈r,x≥4. [NO - the domain includes points
`\leq` 4, also]

d. the function is positive in the interval -[infinity] [YES - all points are positive]