Purple flowers are dominant to white flowers. A heterozygous purple flower is crossed with a white flower. What are the probabilities of the phenotypes and genotypes of their offspring?

Let us assume the following:

From the above assumptions, a heterozygous purple flower would have the genotype Aa, while a white flower would have the genotype aa.

Now, crossing the two flowers:

       Aa    x    aa

   Aa   Aa   aa   aa

From the results of the cross, the offspring's genotypes, phenotypes, and their respective probabilities would be as follows:

In order words, the cross will yield offspring with purple color flower (genotype, Aa) and white flower color (genotype, aa) each with 1/2 probability.

More about monohybrid crossing can be found here: link

50% probability of Pp (purple) or pp (white) genotype.

Explanation:

P = purple gene

p = white gene

Punnet squares show the possible genotypes and probabilities of each genotype in the offspring of a cross:

Purple flower genotype (heterozygous) = Pp

White flower genotype = pp

Punnet Square:

Potential genotypes for offspring are Pp and pp;

According to the Punnett square, 2 of 4 offspring will have the Pp genotype and the other 2 will have pp genotypes;

This means 2 should be purple and 2 white;

Or, there is a 50% chance of having either genotype, of being purple or white.

answer-

the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

solution-

it solely depends on b, whether the function will have one or two or zero x intercept.

this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.

1-   if b is zero, the graph will have exactly one x-intercept, at x= -a

2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ the statement is sometimes true.