STEM Readiness: Pre-Calculus Readiness - Functions/Algebra: Inverse Functions - Finding Domain Restrictions, f?¹(f(x)) = x

Must?Know

• Prokaryotic cells range from 0.1–5.0 ?m in diameter; eukaryotic cells range from 10–100 ?m.
• Prokaryotes include bacteria and archaea; eukaryotes include animals, plants, fungi, and protists.
• DNA in prokaryotes is located in the nucleoid, a region without a membrane; eukaryotes house DNA within a membrane-bound nucleus.
• Prokaryotes lack membrane-bound organelles; eukaryotes contain endoplasmic reticulum, Golgi apparatus, mitochondria, and lysosomes.
• Ribosomes in prokaryotes are 70S (30S + 50S subunits); eukaryotic cytoplasmic ribosomes are 80S (40S + 60S subunits).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, similar to prokaryotes, supporting endosymbiotic theory.
• Cell walls are present in most prokaryotes, composed of peptidoglycan; archaea lack peptidoglycan but may have pseudopeptidoglycan.
• Plant cells have cellulose-based cell walls; fungi have chitin-based walls; animal cells lack cell walls entirely.
• Both prokaryotes and eukaryotes have plasma membranes made of phospholipid bilayers with embedded proteins.
• Eukaryotic cells have internal membrane systems (e.g., nuclear envelope, ER, Golgi); prokaryotes do not.
• Plasmids are small, circular extrachromosomal DNA molecules common in prokaryotes; rare in eukaryotes.
• Prokaryotes reproduce by binary fission; eukaryotes undergo mitosis and meiosis.
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are made of microtubules (9+2 arrangement) and undulate.
• Eukaryotic nucleus contains nuclear pores for regulated transport; prokaryotes lack nuclear pores.
• Nucleolus is present in eukaryotic nuclei and produces ribosomal RNA; absent in prokaryotes.
• Mycoplasma species are bacteria without cell walls, an exception to typical prokaryotic structure.
• Human red blood cells lack a nucleus and mitochondria, an exception among eukaryotic cells.
• Chloroplasts are found in plant cells and some protists; absent in animal and fungal cells.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; rare in plant cells.
• Vacuoles in plant cells are large and central; animal cells have small, multiple vacuoles or vesicles.
• Endosymbiotic theory is supported by mitochondria and chloroplasts having circular DNA, 70S ribosomes, and double membranes.
• Archaea are prokaryotes but have ribosomes and membrane lipids more similar to eukaryotes than bacteria.
• Cytoskeleton (microtubules, microfilaments, intermediate filaments) is present in eukaryotes; prokaryotes have analogous proteins (e.g., FtsZ) but no true cytoskeleton.
• Peroxisomes are single-membrane organelles in eukaryotes that break down fatty acids and detoxify hydrogen peroxide; absent in prokaryotes.
• Glycocalyx (capsule or slime layer) is present in some prokaryotes for adhesion and protection; eukaryotic cells lack this structure.

Difficulty Level

Intermediate – requires distinguishing structural and functional differences across domains and recognizing exceptions.

Common Traps

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacterial cell walls contain peptidoglycan; plants (cellulose), fungi (chitin), and archaea (varied, no peptidoglycan) differ.
Trap: Ribosome size is the same across all cells – Fact: Prokaryotes have 70S, eukaryotic cytoplasm has 80S, but mitochondria/chloroplasts have 70S.
Trap: Eukaryotes are always larger because they are more complex – Fact: Size difference is consistent, but some prokaryotes (e.g., Thiomargarita namibiensis) can be larger than typical eukaryotic cells (verify from standard textbook).
Trap: The nucleus is the only place DNA is found in eukaryotes – Fact: Mitochondria and chloroplasts contain their own circular DNA.
Trap: Prokaryotes have no internal structure – Fact: Prokaryotes have nucleoids, ribosomes, inclusions, and cytoskeletal analogs, but no membrane-bound organelles.

Practice MCQs

Question: Which of the following is a feature found in prokaryotic cells but not in eukaryotic cells?
A) Circular DNA
B) 70S ribosomes
C) Peptidoglycan cell wall
D) Plasma membrane
Answer: C
Explanation: Peptidoglycan is a defining component of bacterial cell walls and is absent in eukaryotic cells.
Why the top distractor is wrong: While 70S ribosomes are common in prokaryotes, they are also present in mitochondria and chloroplasts of eukaryotes, so not exclusive.

Question: Which structure is present in plant cells but not in animal cells?
A) Mitochondria
B) Golgi apparatus
C) Central vacuole
D) Ribosomes
Answer: C
Explanation: The large central vacuole is a defining feature of mature plant cells.
Why the top distractor is wrong: Mitochondria are present in both plant and animal cells for ATP production.

Question: Which of the following provides the strongest evidence for the endosymbiotic origin of mitochondria?
A) Presence of a double membrane
B) Ability to synthesize proteins
C) Containing 70S ribosomes and circular DNA
D) Having their own DNA
Answer: C
Explanation: 70S ribosomes and circular DNA are prokaryotic traits, supporting mitochondrial origin from bacteria.
Why the top distractor is wrong: While double membranes are suggestive, they can form by other mechanisms; 70S + circular DNA is more specific evidence.

Question: Which of the following organisms lacks a nucleus and has 70S ribosomes?
A) Saccharomyces cerevisiae (yeast)
B) Escherichia coli
C) Homo sapiens (liver cell)
D) Arabidopsis thaliana (plant cell)
Answer: B
Explanation: Escherichia coli is a bacterium, a prokaryote with no nucleus and 70S ribosomes.
Why the top distractor is wrong: Yeast is a eukaryote with a nucleus and 80S ribosomes in the cytoplasm.

Question: Which cell type lacks mitochondria?
A) Fungal cell
B) Plant cell
C) Mature human red blood cell
D) Protozoan cell
Answer: C
Explanation: Mature human red blood cells lack mitochondria and generate ATP via glycolysis.
Why the top distractor is wrong: Fungal cells are eukaryotic and require mitochondria for aerobic respiration.

Question: What is the primary component of fungal cell walls?
A) Peptidoglycan
B) Cellulose
C) Chitin
D) Silica
Answer: C
Explanation: Chitin, a nitrogen-containing polysaccharide, is the main structural component of fungal cell walls.
Why the top distractor is wrong: Peptidoglycan is found in bacterial, not fungal, cell walls.

Question: Which of the following is true about the nucleoid?
A) It is surrounded by a lipid bilayer
B) It contains linear chromosomes
C) It is found in prokaryotic cells
D) It houses ribosomal RNA synthesis
Answer: C
Explanation: The nucleoid is the region in prokaryotic cells where circular DNA is located, not enclosed by a membrane.
Why the top distractor is wrong: The nucleoid is not membrane-bound, unlike the eukaryotic nucleus.

Last?Minute Revision

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes: DNA in nucleoid; eukaryotes: DNA in nucleus.
• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA.
• Bacterial cell wall contains peptidoglycan; archaea do not.
• Plant cell wall: cellulose; fungal: chitin; animal: no cell wall.
• Both cell types have phospholipid bilayer plasma membranes.
• Eukaryotes have internal membranes (ER, Golgi, nucleus); prokaryotes do not.
• Mycoplasma lacks a cell wall – exception among bacteria.
• Human red blood cells lack a nucleus and mitochondria.
• Endosymbiotic theory supported by double membranes, 70S ribosomes, and circular DNA in mitochondria.
• Archaea are prokaryotes but have eukaryote-like RNA polymerase and ribosomes.
• Flagellin = prokaryotic flagella protein; microtubules (9+2) = eukaryotic flagella.
• Plasmids = small circular DNA in prokaryotes; rare in eukaryotes.
• Binary fission = prokaryotic division; mitosis = eukaryotic nuclear division.
• Nucleolus synthesizes rRNA – present only in eukaryotic nuclei.
• Lysosomes are common in animal cells; rare in plants.
• Peroxisomes break down fatty acids and detoxify H?O? – eukaryotic only.
• Cytoskeleton (actin, tubulin) is eukaryotic; prokaryotes have FtsZ, MreB, CreS analogs.
• Glycocalyx (capsule/slime layer) is in some prokaryotes; not in eukaryotes.
• Chloroplasts present in plants and some protists; absent in animals and fungi.
• Vacuoles: large and central in plants; small and multiple in animals.
• Nuclear pores regulate transport in eukaryotes; absent in prokaryotes.
• Thiomargarita namibiensis is a giant bacterium (up to 750 ?m) – larger than many eukaryotes (verify from standard textbook).
• Mitochondria are not present in all eukaryotic cells (e.g., mature RBCs, some protists).
• 80S ribosomes are in eukaryotic cytoplasm; 70S in organelles and prokaryotes.